McKinnie arrived at camp Sunday after missing three practices last week. He was subject to a $30,000 fine each day, under terms of the 2011 collective bargaining agreement.
Coach John Harbaugh said he had "a very good conversation" with McKinnie, who attributed his late arrival to a strained back muscle.
"I didn't ask him how he did it," the coach said. "I think he said he fell."
McKinnie completed his physical Monday but did not join his teammates on the field. For that to happen, the 354-pounder has to wait for his back to heal and then pass a conditioning test.
"Like I've said many times, I think the world of B-Mac," Harbaugh said. "I do believe he's a hard worker. I do believe he's been working hard. But he's not ready to practice yet."
Michael Oher has been playing left tackle during McKinnie's absence, and there is no guarantee Oher will return to the right side once McKinnie rejoins the offense.
"My first thought right now is it's going to be a competition. We'll put the best five guys out there," Harbaugh said. "It's not ideal in the sense I'd love for Mike to be settled on one side or the other, but by the same token, that's what it is."
McKinnie starred with Minnesota from 2002-2010 before the Vikings gave up on their former No. 1 draft pick last summer. McKinnie joined the Ravens on Aug. 24 and started every game at left tackle -- considered by many to be the most important position on the offensive line.
With McKinnie helping open holes for Ray Rice and protecting quarterback Joe Flacco, Baltimore's offense ranked 10th in the NFL in rushing, amassed more than 3,500 yards passing and produced the top offensive game in team history in terms of yardage -- 533 in a rout of the St. Louis Rams.
"He's a guy that started 16 games for us last year. He's definitely a big part of this team," wide receiver Anquan Boldin said. "We love having him out there."
Offensive coordinator Cam Cameron said, "We brought him here last year and he filled an unbelievable role for us and really was a big part of us having an opportunity to win."
Cameron did not seem particularly concerned about running the offense without McKinnie during the early stages of camp.
"The season is not tomorrow," he said. "Nobody is worried about it. It will play out the way it should play out, and we will be ready either way."
Meanwhile, tight end Dennis Pitta might have broken his hand during Monday's practice and "needs to get it repaired," according to Harbaugh.
Harbaugh initially guessed Pitta could be sidelined until the regular season opener then backed off that assessment.
"That's very tentative. I'm a little ahead of myself there," Harbaugh said. "I really don't know. But it's not going to be that long. (Tuesday) we could find out it's different because of the MRI. I probably shouldn't have said anything."
Pitta had 41 catches for 406 yards and three touchdowns last season. He split time at the position with Ed Dickson, who had 54 receptions for 528 yards and five scores.