Workers at the city's 15 residential care homes for elderly people and at one home for people with physical disabilities are planning to walk out next Tuesday and Wednesday.
Trade union Unison said their members voted for the action in a bid to stop pay cuts, "unacceptable changes" to job roles and a move to 12-and-a-half hour shifts.
The council say the changes will reduce reliance on agency staff.
A spokesman said the new shift pattern would bring about some changes for staff who currently receive extra payments for working nights.
The move comes after a series of strikes last year by Pupil Support Assistants (PSAs) employed by the city council at Glasgow schools.
As the Evening Times reported at the time, the PSAs walked out over a row about staff having to take on extra duties involving healthcare.
Unison members plan to picket outside the residential care homes during next week's action, which starts at 10pm on Monday.
In a leaflet, Unison said the changes were "totally unacceptable".
The leaflet added: "The council have tried to bully workers into agreeing to the wage cuts and changes on an individual basis."
A council spokesman said the majority of staff had agreed to the proposals.
He said: "We are disappointed with the result of the ballot but it is clear that only a very small proportion of the overall workforce has voted for industrial action.
"Prior to the ballot, 93% of staff had confirmed in writing their agreement with the new working arrangements."