Pedroia left Saturday night's 7-0 loss to the Tampa Bay Rays in the second inning after taking an elbow to the head while attempting to make a tag at second base.
"He's got some symptoms that are consistent with a concussion," said manager John Farrell after the game. "He's improved as the night has gone on here; (he's) not as dizzy as he was when he first came off, but we'll take every precaution necessary with Dustin."
Pedroia was struck in the head by the rising arm of Logan Forsythe as the Rays infielder was sliding head-first into second while advancing on a flyball. Pedroia remained face-down on the field before getting up and being helped off.
"He's a guy that never wants to come off the field, so to see him come off, he's had something wrong," said Xander Bogaerts, who was playing shortstop.
"I didn't even know I really hit him," said Forsythe, "and when I turned back and I saw him down, I felt my arm hit something and I put two and two together."
Farrell said the Red Sox will monitor the situation overnight.
"We've got to be sure that every symptom is clear," he said. "His bell was rung as he was coming off the field. This will be a day to day situation."
Jake Odorizzi and two relief pitchers combined on a one-hitter for the Rays.
Coming off a start Monday night in which he gave up a career-high eight runs over four innings in a 9-1 loss at Baltimore, Odorizzi (10-11) allowed a fourth-inning single to Will Middlebrooks, three walks and struck out seven over seven innings.
Middlebrooks entered the game as a replacement for Pedroia.
Tampa Bay went up 7-0 with a three-run fifth. Two runs scored when catcher David Ross was charged with an error for an off-target throw to first on Brandon Guyer's bunt single.
Webster gave up six runs and five hits over four-plus innings.
The Red Sox loaded the bases with two outs in the seventh when Odorizzi walked three consecutive batters, but the right-hander worked out of trouble by getting a pop fly from Bogaerts.
The start of the game was delayed 12 minutes after a series of stadium lights at Tropicana Field went out during a thunderstorm just before the scheduled first pitch. The Rays said the problem was caused by lightning striking a nearby electrical substation.
Red Sox: Bogaerts was activated from the seven-day concussion list. He missed six games after being hit in the head by a pitch from Seattle's Felix Hernandez August 22.
Rays: CF Desmond Jennings was out of the lineup for the second straight game due to a sore left knee.
The Red Sox announced immediately after the game that they had traded infielder-outfielder Kelly Johnson and infielder Michael Almanzar to the Baltimore Orioles for infielders Jemile Weeks and Ivan DeJesus.