The Health Minister Edwin Poots has said the backlog caused by the Unison strike could take weeks to clear.
Thousands of health and education workers are on a 24-hour walkout in protest at budget cuts.
The Department of Health said that 2,400 appointments or procedures have been cancelled as a result of the action.
Mr Poots said the strike would have an impact.
"People who were in for out-patient appointments, and on the back of that operations would have been set up, will have to wait for a number of weeks before those can be replaced - as a consequence their surgery will be delayed and that is the knock-on effect."
Most of the hospital appointments cancelled in Northern Ireland are for outpatients but some day procedures and elective surgeries have also been postponed.
Mr Poots said the strike action was "avoidable and unnecessary".
He said 87% of Unison members did not vote for strike action and he encouraged them to return to work.
The health minister said it was not "good enough" that operations would be disrupted.
Patricia McKeown of Unison said the situation was "critical" and needed to be put under the spotlight.
She defended the union's right to walk out.
"Many of the people taking industrial action are doing so for the very first time in their lives," she said.
"They've kept the services going in some very, very severe conditions and they are coming to the end of their tether, and they are saying, if we're going to have something here in four years' time when these massive budget cuts have all kicked in, it's not going to look the way it does today."
Sean Donaghy, chief executive of the Northern Health Trust, said while he could understand why colleagues in Unison were taking strike action over funding cuts, it would have a "significant" effect within the trust.
"Each trust, I'm sure, will have its own arrangements to make," he said.
"For example, we're seeing hundreds of patients affected who would normally be accessing our hospital services.
"It has been necessary for us to cancel a range of services, given that staff are not available for those services, as they have opted to take part in the strike action for the day."
The education budget is facing a shortfall of £300m over four years, whilst health is facing cuts of £2.3bn.
The Northern health trust has set up an information line for patients concerned about their appointments.
They can check what services have been affected on 028 2563 3758 or at the trust's website.