As a licensed plumber, I'll reiterate what the two above state about the price, it's not that high relative to the time/material involved.
That aside, it's possible the wet is condensate, exposed water pipes have the "coke can" effect, when running cold water inside they collect condensate outside.
Reach has mentioned the only way you might fix it, and that comes with a caveat - the valve is very old, if you crack or strip the nut while tightening you'll quickly have a flooded basement.
If that doesn't work -
The plumber is going to have to schedule a shut-down with the local water dept, and as Sylvan points out, you need a full port ball valve - the current valve should never have been used. Also, there is no way to seal it externally, especially not while the main is pressurized.
I'd also mention that the copper water main should've been sleeved to protect it from direct contact with concrete, acid in the concrete can eat the copper, that copper inside the mortar could be in rough shape, be careful not to shake or vibrate the pipe if you attempt a fix.