Bridlington Sports Centre has made the decision to close after travellers descended on the site on Saturday evening.
The centre, on Gypsey Road, will be closed until further notice when the situation has been resolved.
A spokesperson from the charity said the group of travellers came onto the site on Saturday evening and members of staff tried to stop more travellers entering on Sunday but eventually "had to back down."
He added: "We are disappointed that whilst trying to operate the charity our staff, volunteers and customers have been victims to assault, criminal damage and arson to the property by a group of travellers who have forced entry to the site and set fires on our football pitches.
"We are still awaiting support from Humberside Police and due to the threats of violence and arson our committee have taken the difficult decision to keep the centre closed until the situation has been resolved.
"This is not a decision we have taken lightly and we are extremely disappointed it has been allowed to get to this stage but we have to put the safety of our customers, volunteers and staff first."