Glasgow Life workers who are members of trade unions are planning to walk out in a dispute over overtime pay and shift patterns.
The strike is set to go ahead two days before the games kick off at Celtic Park, when the city will be packed with athletes and spectators eager to visit tourist attractions like Kelvingrove Art Gallery.
Glasgow Life is an arms-length organisation with more than 2000 staff who run the council's publicly-owned leisure centres, museums and libraries.
A ballot of Unison members closed yesterday and 72% have backed industrial action.
Unison City of Glasgow Branch Secretary Brian Smith said: "The unions met late on Friday to plan industrial action for the week beginning July 21.
"The unions remain willing to talk to Glasgow Life in an effort to resolve the dispute, however the employer has not made contact with us.
"This is a situation that will affect the Commonwealth Games. You'd think they'd want to cut a deal."
Unite members also voted for action but the margin was "slight", according to Regional Industrial Officer Willie McGonigle.
He said: "We'll still be looking for our members to support the industrial action, given Unison's result."
The results of a ballot of members of the GMB who work for Glasgow Life are expected on Monday.
A spokesman for Glasgow Life said: "The number of Unison members balloting for strike action represents just 2.4% of our entire workforce and less than a third of the members eligible to vote, took part in the ballot.
"We do not believe this provides any reasonable justification to embark on strike action at any time, let alone in the build up to the biggest sport and cultural celebration the city has ever seen.
"Many of our staff remain proud to be part of the team delivering the Glasgow 2014 Commonwealth Games and we will do everything possible to minimise disruption."