Besides serving as a place of worship and community center, the mosque in Bloomington, just south of Minneapolis, has a fitness center, gymnasiums for boys and girls, a football field and adjoins a city park, Omar said.
The number of anti-Muslim hate groups in the USA has almost tripled since Trump launched his presidential campaign in 2015, according to the Southern Poverty Law Center.
Police say there were no injuries, but the explosion damaged the imam's office.
Minnesota Governor Mark Dayton visited the mosque on Sunday, describing the bombing as "so wretched" and "not Minnesota".
Jaylani Hussein, the executive director of the Minnesota chapter of the Council on American-Islamic Relations said that thankfully it was not the Ramadan time; otherwise the explosion would have definitely injured the people who came to the mosque to offer their prayers.
"This could have been very big and very damaging", said Asad Zaman with the Muslim American Society of Minnesota.
"Through his Muslims ban and comments from the campaign trail, he has instead painted the entire American Muslim community as suspect".
Federal Bureau of Investigation officials in Minneapolis are investigating the incident and declined to provide further details on Sunday. The FBI is offering a $24,000 reward for information leading to the arrest of the culprit, NBC reported.
Omar also said his community was grateful for the support it had received since the incident, including from other religious groups, with visitors continuing to drop off flowers and donations.
Trump's silence on the attack follows similar periods of quiet after the January shooting at a mosque in Quebec that left six dead, the murder of a Muslim teenager in Virginia and the Finsbury Park mosque attack in London that left one dead, both in June.
The center's executive director, Mohamed Omar, told NBC that the bomb was allegedly tossed into the mosque from a pickup truck.
A May analysis by the Council on American-Islamic Relations found 2,213 anti-Muslim bias incidents in the United States a year ago, up 57 percent from 2015.
"There's two things at play: the outpouring of support and the actor behind this attack", says Montemayor. "You have to check them and find out who the perpetrators are".