The Labour peer fears the sporting event in July and August - which is due to end just over six weeks before voters go to the polls - could be overshadowed by political rows.
Scottish badminton player Susan Egelstaff is among some competitors who have already expressed concern that the event could be tainted by political point scoring.
The peer will use a debate on the Games in the Lords later today to call for a two-week ceasefire.
He said: "It is important for the athletes, the organisers, the cultural performers and all those involved in the Commonwealth Games that any worries that the Games could be used for political purposes, by either side, are tackled and tackled right now.
"Both sides need to state clearly that there will be a truce during the Games; that there will be no campaigning and no exploitation of the Games or those involved."
He warned that not calling a truce risked damaging the preparation of the Games and jeopardising the benefits it could bring to Glasgow and Scotland.
He said: "The risk is that the athletes and performers are worried instead of concentrating on doing their very best, winning medals and selling Glasgow and Scotland to a global audience."
He also highlighted a precedence for such a move. Campaigning during the 1997 devolution referendum was halted for a number of days following the death of Princess Diana.
Lord McConnell, who led the Yes Campaign at the time, said the 1997 experience proved a truce "might be difficult to achieve, but it can be done".
Last night a Yes Scotland spokesman said: "This is an interesting idea, although perhaps a little unrealistic especially from a former First Minister.
"The Commonwealth Games, of course, promise to be a wonderful spectacle to be enjoyed at home, throughout the rest of the UK and overseas and will showcase Scotland at its best.
"But we are also engaged in a vitally important debate about the future of our nation and there is no reason why we cannot enjoy the Games while continuing to weigh up the two futures on offer."
A spokesman for the pro-Union Better Together campaign said: "While we don't think that campaigning will stop completely, it would be fair to say that the people of Scotland will be much more interested in the sporting action that will be taking place during the Games."