Veteran's Memorial Park was under surveillance when Allen, R-Merritt Island, was seen coming in and out of a restroom three times, Lt. Todd Hutchinson said.
Allen, 48, then approached an undercover officer and was arrested.
He has been charged with solicitation for prostitution, which has a maximum penalty of one year in jail. Brevard County jail officials said Allen posted a $500 bond.
An e-mail sent to Allen and telephone messages left by The Associated Press on his cell phone and at his office were not immediately returned. It was not known if he had an attorney.
While being transported to jail, Allen told WFTV Channel 9 that the situation was "a very big misunderstanding."
Allen, a married father of one, was elected to the Florida House in 2000. He was chairman of the House Committee on Energy.