Newton was asked a question by reporter Jourdan Rodrigue of the Charlotte Observer and smirked before delivering a response for which he was immediately condemned.
"It's funny to hear a female talk about routes."
The former NFL MVP was almost immediately dropped by sponsor Dannon for the incident.
He later used Twitter to post a video apology.
"After careful thought, I understand that my word choice was extremely degrading and disrespectful to women," Newton said.
If you are a person who took offense to what I said, I sincerely apologise to you.
"I'm a father to two beautiful daughters, and at their age I try to instill in them that they can do and be anything that they want to be.
"During this whole process I've already lost sponsors and countless fans, I realise that the joke was really on me. And I've learned a valuable lesson from this."
The backlash has continued following Newton's controversial comments across the NFL.