The 38-year-old singer and actor issued an apology Wednesday on Instagram after he was spotted holding hands with his Palmer co-star Alisha Wainwright in November.
"I stay away from gossip as much as I can, but for my family I feel it is important to address recent rumors that are hurting the people I love," Timberlake wrote.
"A few weeks ago I displayed a strong lapse in judgement - but let me be clear - nothing happened between me and my costar. I drank way too much that night and I regret my behavior. This is not the example I want to set for my son."
Timberlake and Biel married in October 2012 and have a 4-year-old son, Silas Randall.
"I apologize to my amazing wife and family for putting them through such an embarrassing situation, and I am focused on being the best husband and father I can be. This was not that," Timberlake said.
"I am incredibly proud to be working on Palmer," he added. "Looking forward to continuing to make this movie and excited for people to see it."
The Sun published photos and videos Nov. 23 of Timberlake, Wainwright and a group of friends at a bar in New Orleans. Timberlake appears to hold Wainwright's hand as the actress rests her hand on his knee.
Sources told People in November that Timberlake and Wainwright's interaction with "completely innocent."
"It was nothing. They're starring in the movie together and they're cool," an insider said.
Timberlake and Wainwright play Eddie Palmer and Maggie Hayes in Palmer. The movie is directed by Fisher Stevens and co-stars Ryder Allen.