Last week, photos circulated online of the 38-year-old actor appearing to get cozy and flirty with his "Palmer" co-star Wainwright.
According to The Sun, who first reported the news and obtained photos, the co-stars were seen taking a break from filming and hanging out at a New Orleans bar late at night.
Images showed the 30-year-old actress placing her hands on Timberlake's knee and they were seen touching each other's hands.
Now on Thursday, Timberlake took to Instagram and posted a lengthy statement, apologising to his wife, reports metro.co.uk.
"I stay away from gossip as much as I can, but for my family I feel it is important to address recent rumours that are hurting the people that I love. A few weeks ago I displayed a strong lapse in judgement - but let me be clear - nothing happened between me and my co-star."
"I drank way too much that night and I regret my behaviour. I should have known better. This is not the example I want to set for my son," he wrote.
Timberlake is now focusing to be the best husband and father.
"I apologise 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. I am incredibly proud to be working on 'Palmer'. Looking forward to continuing to make this movie and excited for people to see it," he added.
( With inputs from IANS )