Shaun Livingston replaced Thompson in the starting lineup for the Warriors to make his second start in the postseason. Livingston has played in all 18 playoff games, averaging 4.1 points.
It marks the first time in Thompson's eight-year career that he has missed a playoff game -- a span that covers 120 straight playoff games.
Warriors officials preferred to have Thompson sit out to protect his sore hamstring for the rest of the Finals, but Thompson continued to lobby them to play, league sources told ESPN's Ramona Shelburne and Adrian Wojnarowski.
Thompson injured his hamstring in the second half of the Warriors' Game 2 victory in Toronto on Sunday night. He was unable to return to that contest.
An MRI revealed a mild strain, and Thompson officially was listed as "questionable" for Game 3.
Thompson said Tuesday it's "a game-time decision, but personally it's hard to see me not playing," then added, "If there's any pain, it will be a no-go, because of the position we are in. This could be a long series."
"He thinks he'll be ready to go," Warriors coach Steve Kerr said Tuesday. "But as I said the other night, Klay is always going to say he's ready to go. What we'll have to determine is, is that a risk? If he plays, are we risking anything?"
Durant continues making progress toward a return, potentially as early as Game 4 in Oakland on Friday. Durant hasn't played since injuring his right calf May 8 against the Houston Rockets in the Western Conference semifinals.
"He had a really good workout yesterday," Kerr said of Durant on Wednesday before Game 3. "Ramped it up, and it went well. He had another one today; it went well. So we would like to increase it tomorrow, meaning get other people involved; he hasn't played any 3-on-3, 5-on-5."
Kerr said before Game 2 it was "feasible" that Durant could participate in just one practice and be cleared to play in a game. While Kerr noted that the Warriors wouldn't have a regular practice the day after a game, he did say Durant likely would participate in some scrimmages with various members of the Warriors staff following a team film session.
"We probably won't practice, practice as a team, tomorrow," Kerr said. "It will be a film session and a walk-through. So if possible, we'll get him together with some of our young guys, maybe a few of our coaches and try to get him out on the floor. That would be the next step."
Kerr certainly sounded optimistic that Durant would be able to play if he continued making improvements in his rehab.
"He's got to continue to improve and not have any setbacks," Kerr said. "That's the main thing. So we'll go from there."
ESPN's Nick Friedell contributed to this report.