(I'm not an application programmer, so take this with a grain of salt) A web application can not open a program on a users desktop, unless it is using a protocol/URI (i.e. Outlook's mailto: protocol, BitTorrent's magnet: protocol). Minecraft doesn't have a protocol like that, and Java can't do that either.
To add on to what StealthBravo explained above, it would be incredibly concerning if you were actually able to do what you wanted. The security risks associated with actually being able to do that far outweigh the benefit of skipping the two step (Ctrl-C Ctrl-V) process in copying the server IP over to Minecraft.