Unison said a survey of more than 4,000 staff in care homes and those working in the community suggested that plans for mandatory vaccinations would be counterproductive and could trigger people leaving a sector which already has a staffing crisis.
The union has detailed its concerns in evidence to a Government consultation on proposals to make the jab compulsory for workers in care homes.
Almost nine out of 10 respondents said they had been vaccinated so far.
The most common responses from non-vaccinated staff was pregnancy, waiting for more research before going ahead or because they were still waiting for an appointment.
More than two-thirds of those who took part in the survey said their employer had provided support and advice about the Covid-19 vaccine, but others had received no helpful advice from their bosses – and some claimed employers had imposed a deadline for them to get the jab.
A minority said their employer had threatened to sack them if they turned down the offer of a vaccination, or they were told their pay would be cut if they refused.
Unison senior national officer for social care Gavin Edwards said: "Vaccinations are the way out of this pandemic, but forcing staff to get jabbed won't work, nor will threats and bullying.
"The Government should concentrate on persuasion and reassurance. The care sector is facing huge staff shortages and this will only get worse if employees feel coerced and unsupported."