Officials said security camera footage showed two white males placing the flags on the ground at the church.
They were discovered by maintenance workers on Thursday morning. One of the church's pastors said it was "a hateful act" meant to intimidate churchgoers.
The flag is very divisive in the US and seen as a symbol of slavery by critics.
Staff were disturbed when they came across the flags at the Ebenezer Baptist Church, according to the Reverend Shannon Jones.
"Our groundsmen were so upset, they took pictures and then they moved them," she told reporters.
She said the church has been holding a conference on the role of black churches in social justice issues this week.
"We do have images of two white males placing those flags on the campus," police chief George Turner said at a news conference.
There were no more details about the suspects but Mr Turner said the video would be released to the public soon.
"We've seen this kind of ugliness before," he said, adding that it was disgusting but not surprising.
He said they had "good, strong physical evidence" and were not ruling it out from being a hate crime.
Rev Raphael Warnock, a senior pastor at the church, said: "It is a hateful act. I view it as an effort to intimidate us in some way, and we will not be intimidated."
Mr King once preached at the church in Georgia's capital.
The Confederate flag is the battle emblem of the southern states in the US Civil War, and its supporters today say it is an important part of southern heritage.
The backlash against it grew when nine black people were shot dead at a South Carolina church in June. The man charged with the killings, Dylann Roof, was pictured holding the flag.

Needing another 132 for victory with eight wickets in hand on the final day at Grace Road, Wells finished unbeaten on 90 as Sussex strolled home on 234-5.
Anchored by Wells' 190-ball innings, Sussex never looked in any trouble despite losing three wickets.
Sussex have now won back-to-back games, while Leicestershire are still winless.
Their successive victories have come under new captain Chris Nash after Luke Wright stepped down from the role at the start of the month.
Wells has been instrumental in both wins, scoring 155 in the innings victory over Worcestershire, before his match-winning knock in this game.
Sussex head coach Mark Davis told BBC Radio Sussex:
"In our other two wins this season we've been ahead of the game - but here we've come from behind to show loads of character, skill and guts. It was nice to see.
"A couple of individuals will take the headlines, but it was a proper team performance."
US police are investigating after four Confederate flags were found on the grounds of a church near the Martin Luther King Jr Center in Atlanta.
[NEXT_CONCEPT]
Luke Wells continued his superb batting form to guide Sussex to a five-wicket win over Leicestershire in Division Two of the County Championship.