Kemp, who stars in TV drama Eastenders, received a "thick lip" in the incident, which took place at their south London home in the early hours of this morning - according to the Metropolitan Police.
Wade, the editor of The Sun - which is owned by media magnate RUPERT MURDOCH - has been released without charge.
The pair married in Las Vegas in 2002.
Kemp recently returned to the popular BBC soap after six years - playing hardman GRANT MITCHELL.
He also appeared in the first series of Ricky Gervais' lastest comedy series EXTRAS.