The FBI are searching for a perpetrator who threw an improvised explosive device through the window of an imam's office at the Dar Al Farooq mosque in Bloomington.
Police were called shortly after 5am on Saturday following reports of an explosion as worshippers prepared for morning prayers.
The blast damaged a room and shattered windows, but no one was hurt.
Minnesota governor Mark Dayton on Sunday morning visited the mosque and described the bombing as a "criminal act of terrorism".
He also described it as a "unthinkable, unforgivable" hate crime.
"What a terrible, dastardly, cowardly act was committed," he said.
Meanwhile, Mr Trump came under heavy fire for staying silent on the issue.
"The moment the smallest attack happens at an evangelical church in the US, Trump will stop everything and get on TV, but a mosque — silence," said one Twitter user.
The FBI is trying to determine whether the incident was a hate crime, while Islamic leaders said the bombing had left them fearful of future attacks.
"We feel like it's much deeper and scarier than like something random," said the mosque's director, Mohammed Omar. "It's so scary."
The mosque opened in 2011 at the site of a former elementary school and serves people primarily from the area's large Somali community. Minnesota has the largest Somali community in the US, roughly 57,000 people, according to the latest census figures.
The US Department of Homeland Security on Saturday released a statement saying it "fully supports the rights of all to freely and safely worship the faith of their choosing and we vigorously condemn such attacks on any religious institution".
The bombing came amid increased reports of anti-Muslim crimes, including arson attacks and vandalism at mosques.
Last week, an Islamic cemetery in Minnesota was sprayed with profanities and swastikas. One spray-painted message reportedly said: "Leave, you R dead."
The Council on American-Islamic Relations has offered a $10,000 (£7,700) reward for information leading to the capture and conviction of the bomber. It has called for mosques and Islamic centres to improve their security in the wake of the attack.