AVONIEL Leisure Centre was forced to shut on Sunday after an incident in which the gates were blocked.
Belfast City Council confirmed a group of men "barricaded and locked the entrance gates".
The council decided to close the centre and divert customers elsewhere.
The centre typically is open from 10am to 4pm on Sundays.
A bonfire has been built in its car park ahead of the Eleventh night celebrations.
SDLP councillor Séamas de Faoite said it was "entirely unacceptable that staff and customers would be barricaded out or threatened".
Sinn Féin's Ciaran Beattie said such behaviour was "absolutely reprehensible".
Michelle Kelly of Alliance said rubbish had been placed across the entrance to the centre, forcing its closure.
"It is believed to be in relation to the bonfire on the site," she said.
"It is totally unacceptable anyone would do this for any reason and force the temporary closure of any council facility."
Green Party councillor Anthony Flynn described it as a "sinister development".
"The leisure centre is a community asset and it's clear that those behind this are anti community and self serving," he said.
"I would call on the police to take robust action against these people and assist council to have the leisure centre reopened."
The leisure centre was open at 7.15am for business as usual on Monday morning, although the main gates to the car park remained closed later in the morning after a chain and padlock were placed around the gates.
The chain was later removed and the gates opened.
A spokesperson for the East Belfast Cultural Collectives, which represents 13 bonfires, including Avoniel, said bonfire builders "did not threaten or intimidate anyone".
