The law says that a Senator can be suspended by a Governor. Then a Senate review is necessary to remove him. Here is the law:
Committee on Ethics and Elections
Governor's Executive Orders (Including Suspensions)
The Suspension Process
"The Senate is constitutionally charged with the duty to review the Governor's executive suspensions and, upon such review, either reinstate the suspended official or … remove him from office. Although the Governor has exclusive authority to initiate suspensions, the Senate has the responsibility to make final dispositions of them. The Senate is entrusted with the great duty and responsibility to ensure that the awesome executive power of suspension is used to achieve its constitutionally intended public purposes and to see that no officer is removed for grounds other than those provided by law."1
Article IV, section 7(a), of the State Constitution authorizes the Governor to suspend any state officer not subject to impeachment or any county officer on any of the following grounds:
Neglect of Duty;
Permanent Inability to Perform Official Duties; or,
Commission of a Felony.
The Legislature has enacted procedural statutes which broadly address the executive suspension and removal process in Part V, Chapter 112, Florida Statutes. Additional procedures are contained in Senate Rule 12. Pursuant to these statutes and rules, public officers are provided a full and fair hearing on the facts, in a manner appropriate to the case, prior to any final Senate act.