Authorities in Bloomington said no one was injured in the blast at the city's Dar Al-Farooq Islamic Center.
An improvised explosive device caused the explosion, the FBI office in Minneapolis tweeted Saturday afternoon.
Another tweet said the FBI is working on determining who set off the explosive and why.
The FBI is the lead investigative agency. Police are asking anyone with information to contact the FBI.
Deputy Chief Mike Hartley of the Bloomington Police Department said officers received a report about the explosion around 5 a.m. (6 a.m. ET) Saturday. Responding officers found damage to the building and smoke in the area, the police department said in a tweet.
At a news conference Saturday, a witness said the explosion happened around the time of morning prayers. The witness described running outside after the blast and seeing a car driving away.
A spokesman for the Muslim American Society of Minnesota
told CNN affiliate WCCO
the group believes someone may have thrown something into the window of the mosque imam's office.
The society's executive director, Asad Zaman, said the imam's window was broken and cited a witness who saw someone standing by the window before the explosion.
The Minnesota chapter of the Council on American-Islamic Relations
is offering a $10,000 reward in the case.
"If a bias motive is proven, this attack would represent another in a long list of hate incidents targeting Islamic institutions nationwide in recent months," said Amir Malik, CAIR's civil rights director in Minnesota.
Law enforcement authorities have not said whether they are investigating the mosque explosion as a hate crime.
The US Department of Homeland Security said 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. We are thankful that there were no injuries, but that does not diminish the serious nature of this act."