Investigators say David Conrad, 51, lives next to the mosque in Morton Grove. They say he fired a pellet rifle at the building while 500 people prayed inside Friday evening and damaged the mosque.
The shooting happened after worshippers observing Ramadan broke their daily fast.
No one was wounded Friday, but a Muslim civil liberties group subsequently said the shots damaged an outer brick wall of the center. Worshippers inside reportedly heard the shots.
"This is obviously an alarming situation," said Ahmed Rehab, director of the Chicago branch of the Council on American-Islamic Relations (CAIR). "The weapon allegedly used in this incident is powerful enough to kill, and the projectiles reportedly came within inches of the head of the security guard on duty."
The Muslim advocacy group said it believed the shots were fired by someone with a history of opposition to the mosque. It did not elaborate.
Morton Grove Police Chief Mark Erickson Erickson said police were told Friday night that windows at the mosque previously had been broken, but not reported.
Upon taking Conrad into custody, police also seized a high-velocity air rifle outfitted with a scope in connection with the shooting at the Muslim Education Center, authorities said Sunday.
The police statement gave few details and did not elaborate on the time or place of the arrest. But it said investigators found Conrad after being directed to an area just east of the Muslim Education Center property.
An email statement released early Sunday by Morton Grove Police Cmdr. Paul Yaras said Conrad had been charged with three felony counts of aggravated discharge of a firearm and one felony count of criminal damage to property.
It was not immediately known if Conrad has a lawyer. A bond hearing was scheduled Monday, police said, adding a subsequent Aug. 22 court appearance was planned.
Morton Grove police, contacted by The Associated Press by telephone early Sunday, said they would have no further details immediately about the case.
CAIR's national headquarters issued a community safety advisory earlier in the week for American mosques after other incidents targeting Muslim houses of worship in Missouri and Rhode Island and after the deadly shooting at a Sikh temple in Wisconsin on Aug. 5.
In one of those incidents, a mosque in Joplin, Mo., previously targeted by an arsonist burned down. In Southern California, pig legs were left in the driveway of a house used as a place of worship pending construction of a mosque on the site in the city of Ontario -- an offensive act because Muslims regard pigs as unclean.
(The Associated Press contributed to this report.)