More than 8,000 members of the GMB and Unison unions are talking part in the 48-hour industrial action on Tuesday and Wednesday.
Thousands of female workers are proceeding with equal pay claims against the council following a Court of Session ruling last year.
GMB Scotland organiser Rhea Wolfson said the action aimed to bring the city to a “standstill” to progress negotiations.
The council said “there is nothing that the strike can achieve that we are not already doing” on equal pay.
It said it had been exploring all options to prevent the walkout and accused unions leaders of reneging on an agreement “on providing life and limb cover for our most vulnerable citizens”. The unions have denied that claim.
It said letters had been sent to those affected informing them their care will be withdrawn during the strike.
All nurseries and primary schools will be shut on both days, but secondary schools will remain open.
A spokeswoman for Glasgow City Council said: “We understand why many of our workforce are angry about equal pay and we are also very aware of the depth of feeling there is behind this industrial action.
“However, the council is already committed to delivering equal pay and reaching a negotiated settlement on claims.
“There is nothing that the strike can achieve that we are not already doing and we are anxious to see everyone back around the table in good faith to move things forward.
“At the same time, the way union leaders have approached the strike has been hugely disappointing. We believed we had an agreement on providing life and limb cover for our most vulnerable citizens – indeed, the unions told the public that cover would be in place.
“There has been absolutely no meaningful effort from the unions to work with us and their membership to ensure that life and limb cover will be in place.”
The GMB union said the offer from union members to work through the strike to support vulnerable home care users still stands.
Ms Wolfson said: “The council’s officers have been incapable of putting in place the most basic cover despite having three weeks to prepare and the offers we have made every single day to resolve the dispute.”
She added: “Our members work for some of the most vulnerable elderly and disabled people in our community and we would never do anything that could cause them harm.”