Surveillance cameras caught the man in action Sunday morning at Pilgrims United Church of Christ.
The church has a reputation for supporting gay rights and has been targeted in the past.
"Obviously, we're looking at a crime of sexual orientation, especially given recent events in our state," Maple Grove Police Captain Keith Terlinden told CBS Minnesota.
The state will legally recognize gay marriage as of Thursday, August 1.
The video shows the man throwing eggs at the church. What wasn't seen on tape is the graffiti he allegedly wrote on church walls, making his anti-gay feelings known.
"At this point, it doesn't appear the person responsible for this damage is someone that's associated with church," Capt. Terlinden said.
This is the third time Pilgrims United has been targeted. Similar vandalism happened twice in June, and police think the same person is responsible for all three incidents.
Police stepped up patrols in the area northwest of the Twin Cities in fear of more property damage when same-sex couples can legally marry.
The church has said it would host those same-sex marriage ceremonies.