He wrote on Instagram: “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 behaviour. I should have known better. This is not the example I want to set for my son.
“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.”
Timberlake and Biel tied the knot in October 2012 and share four-year-old son Silas.
He and Wainwright, 30, were drinking at a bar during a break in filming for Palmer last month in New Orleans.
The pair play lovers in the drama, which is directed by Fisher Stevens.
