At least one window was smashed at the Islam Care Centre on Somerset Street West.
On Friday, a piece of cardboard covered part of the broken window on the door to the main entrance. A notice on the building says it is monitored by 24-hour video surveillance.
A window at the Ottawa Mosque on Northwestern Avenue was also shattered. Both incidents happened on Wednesday.
In a media release, police said they received a phone call on Wednesday from a man who wanted to turn himself in and that during the arrest he allegedly assaulted one of the arresting officers.
The man was later charged with two counts of mischief and one count of assaulting a police officer.
Ottawa Muslim Association president Naeem Malik said in a statement on the mosque's website that no injuries were reported.
"It's always distressing to see our places of worship targeted in this hateful way. We call on the police to investigate these incidents as potential hate crimes," Malik said. "We know that such acts do not represent the sentiments of our fellow Ottawa neighbours and community members."
Omar Mahfoudhi, executive director of the Islam Care Centre, was also quoted in the statement, urging residents to report suspicious activities to the police.
Ottawa police did not say whether or not the vandalism is being investigated as a hate crime.
On Tuesday, the Ottawa Police Service announced residents are now able to report hate crimes on its website.
Earlier this year, the city saw a spate of racist and Islamophobic graffiti attacks targeting multiple mosques and other religious buildings. A 17-year-old boy was charged in those incidents and has since pleaded guilty to the crimes.
Following the attacks, dozens of people formed a human chain around the Ottawa Mosque to show solidarity with the local Muslim community.