The Lightning said Hedman is day-to-day, and coach Jon Cooper told reporters that the veteran was "definitely a little bit more sore than we anticipated."
Hedman missed around half of the first period in Saturday's game at the San Jose Sharks after being checked hard in the corner boards.
The 2018 Norris Trophy winner sat out Monday's practice and had limited participation during Tuesday's morning skate that included no involvement in power-play drills.
A finalist for the Norris Trophy in each of the past six seasons, Hedman has one goal and eight points in nine games this season. Haydn Fleury, a healthy scratch in five of the previous six games, replaced Hedman on the game roster.
Without Hedman, Nikita Kucherov had a goal and two assists as the Lightning rallied past the Senators.
Tampa Bay went ahead to stay when Kucherov scored from the low right circle with 2:30 remaining off a cross-ice pass by Mikhail Sergachev. Kucherov has a four-game goal streak and an eight-game point streak overall.
Tampa Bay scored three of the four goals between the teams over the final 8:56 of the game.
"It was a wild one," Cooper said. "No doubt about it."
The Associated Press contributed to this report.