"It's not going to be a season-ender by any stretch," Harbaugh said. "How many weeks it is depends on how fast it heals. We'll see going forward."
Harbaugh described the injury as a Grade 2 sprain, which typically takes two to four weeks to recover.
Asked if Smith could be a candidate for injured reserve-designated to return, Harbaugh said, "It's a possibility. I don't think it's a probability right now."
Smith, considered the Ravens' second-best corner, is in the final year of a four-year, $41.1 million contract.
Anthony Averett, a fourth-round pick in 2018, is expected to start in Smith's place. Averett was picked on early by the Dolphins, but he finished second on the Ravens with four tackles.
Harbaugh complimented Averett for his tight coverage.
"Once he got his sea legs, he really played well," Harbaugh said.
Baltimore's secondary was once its deepest position. But nickelback Tavon Young suffered a season-ending neck injury in training camp, and now Smith will be sidelined for a stretch.
Over the next four games, the Ravens will face notable quarterbacks in Kyler Murray, the No. 1 overall pick in this year's draft, Patrick Mahomes, the reigning NFL Most Valuable Player; Baker Mayfield, who threw for over 340 yards in each of his two meetings with Baltimore; and Ben Roethlisberger, who has won four of his past five meetings against the Ravens.