We’ve just bought a new MacBookPro Retina 13" Late 2013 and when plugging in an external monitor to the thunderbolt port using a 3rd party mini display port to DVI adapter, the wifi drops away and the internet becomes more or less inaccessible.
Change the router’s wifi channel to the lowest possible number, such as 1.
The problem with a little more detail
I was wondering why the internet was running so slowly, so tried to bring up the speedtest website. I figured perhaps there was an issue with the Wifi where the laptop was sitting, so unplugged all the cables to move it, and miraculously speeds returned.
As soon the monitor was plugged in, speeds would drop to nothing. As soon as it was unplugged, speeds would go back to normal. Trying a different monitor with a VGA adapter worked fine. Going back to the same monitor with DVI caused issues.
(I can’t remember now if I tried VGA on the troublesome monitor or not, but guess now it must have had issues because I continued to use the different monitor.)
The solution with a little more detail
I found this thread at the Apple Support Communities where a lot of people were talking about issues with wifi and changing the channel to a lower number solved the problem. They also suggested using the 5 GHz channel, but my router doesn’t support this.
This seemed a fairly unlikely solution to me, but I decided to try it anyway. The channel the router had been set to was 6, so I manually dropped it to 1. And it solved the issue; speedtests were now back to the normal levels with the monitor that had been having issues.
This is a weird problem with a weird solution. I hope it works for you too.