I think I have a virus?

After surfing suddenly a popup window appeared telling me I have an infection and to call 1-855-751-2034. I can't open Safari without this window popping up.
Does anyone know whether this is a legit number for Apple, or whether this is a virus? There was also a link to an address, but I didn't use it.

This sounds like a browser hijack to me. If so, it's not a virus but it is annoying to say the least. Try the following and see if it helps:

1. Turn off wireless networking if you have it on.
2. Disconnect the ethernet cable if you are using that to connect to the Internet.
3. Close whatever browser you are using.
4. Reopen the browser and close the window where the message appears. While you are there dump the browser cache.
5. Reconnect to the Internet and open the browser. The problem window should be fine.

Thanks for your reply, but I'm not familiar with tech terms.
But, yes, I have wireless. My laptop is opening Safari with no problem.
Which is the ethernet cable? (Sorry, I'm not savvy!)
I was using Safari, and I have to force closed it.
After force closing, when I reopen Safari I get the same window with the alert and have to force close to get rid of the window again.

The reason you arrogating the same window is that when Safari re-opens it remembers the last page you were trying to view. As that page loads the same window reappears and the whole mess all over again.

Here's a simpler method try it and see if it works:

Force quit Safari. Then when you launch it again hold down the shift key. This will prevent windows from the last session from opening. The ethernet cable will run out of the side or back of the computer. It is listed as gigabit ethernet in this image.

And then it sounds like you need to download and run AdwareMedic that you can get from here:
AdwareMedic

You don't have a virus (since such a thing doesn't exist on a Mac), but you DO have adware. Download the Adware Medic app from adwaremedic.com, that should fix it right up. If it does, shoot the guy a donation.

You do not need to download Adware Medic in this case. There is nothing installed on the users machine. The op couldn't download it if they wanted to without using a different browser. Safari is stuck in a loop because when you force quit Safari, it reopens the same tabs you already had open and takes the op right back to the same site that has the browser hijacker.

These nasties work similar to the sites where when you try to close the tab they have a popup that asks are you "sure" you want to leave this page.

Slydude already gave the correct answer(s).
1. After you quit Safari... disconnect your computer from the internet.

Since you are using wireless...
Click on the Network icon at the right side of the Menu bar at the top of the screen and then select "Turn Wi-Fi Off".

Then open Safari and just close all the tabs or quit Safari normally - not force quit.

You can then turn your wi-fi back on.

2. Hold down the shift key while starting Safari so that it won't load the previous windows. (Not tried this one - Have to remember this next time I run into one of these nasty boogers.)

3. You can actually do it without disconnecting from the internet if you are fast enough - after opening Safari again - to close the offending tab before it can load.

Running Onyx would likely work also if you have it remove all browser history.

Thank you all! To clarify: My Mac Mini is connected to my router, running Mavericks 10.9.5, and am using a tv monitor for a screen (not subscribed to tv). Please tell me how to identify the ethernet cable on the Mini? Then I'll be able to try your suggestions. Also, what is the difference between the cache and cookies? And, how do I delete the cache?

How is your Mac Mini connected to your router? If by wire, that's the Ethernet cable. If wireless, then use the process bobtomay described in post #7. Cache is a store of recently visited websites that browsers use to speed up the process of displaying the site for you. The browser reaches into cache if you return to the exact same website and puts that up while the "real" data is still downloading. Cookies are small files that websites put on your computer to "enhance" your browsing experience by remembering things you do, accounts, passwords (sometimes) and also to track what you do, where you go, what you look at, what to click on, etc. Some cookies are good, some are not so good, some are just plain evil. You CAN delete cookies, but then places like Facebook, and here, won't "remember" you next time. You can log in and it will replace the cookie and start remembering you again.

Hello MacInWin, I have 4 cables connected to my Mini: the wireless slot, HDMI slot, the other two I don't know. A short horizontal line with an arrow at each end? And a short, horizontal curve line.

If there is a wire connected to the double-header arrow, that is the Gigabit Ethernet port. The other end of that cable would be in your router. The connector should have a little catch that holds it in the socket. I downloaded a picture of a mac mini ports from 2012 here. The ethernet port is labeled in the lower left corner with the symbol. Also check on the desktop that the fan shaped icon on the top bar is empty, with no black bars in it. That's the wireless indicator. Assuming those are as described, you can disconnect the ethernet and be out of the internet.

Ok, going to try it now!

The ethernet cable would go from your Mac to your router/modem. Since you say that you are connected to the internet by wireless, it's unlikely you have an ethernet cable connected.

The ethernet socket on a Mini is shown here:

Aw, that's cheating MacInWin. You posted while I was typing.

Safari is back to normal now. It worked like a charm! I can't thank you enough--all of you for your patience, and instructions!
I've copied your posts just in case this should happen again.

Great! Now go get AdBlock+ or Ghostery and use them to keep it from happening again.