Cooper's comments came as fellow Tory, Jacob Rees-Mogg, on Saturday suggested a Conservative Party investigation into Johnson was a "show trial" being used to stop him becoming the next party leader.
Furthermore, Rees-Mogg implied that Mrs May's actions were only helping Labour: "When Margaret Thatcher was Leader, she and Michael Heseltine were hardly soulmates but she would not have allowed personal rivalry to take the heat off the Labour Party". However, there has been a mass outpouring of support for his comments in which he compared women who wear the Burka and Niqab to "letterboxes" and "bank robbers".
A panel including one independent figure, one representative of the voluntary party and one nominated by the backbench 1922 Committee, will look into complaints that Mr Johnson's comments breached the Conservative Party's code of conduct.
He added that he "entirely agrees" with Johnson and suggested he was under attack because of "envy" over his "many successes, popularity with voters and charisma".
"Could it be that there is a nervousness that a once and probably future leadership contender is becoming too popular and needs to be stopped?".
Mr Johnson, who is holidaying overseas, is yet to respond to the furore sparked by his article on Monday in which he said Muslim women wearing the burka looked like "letter boxes" or bank robbers.
'This may explain the attempt to use the Conservative Party's disciplinary procedures, but it has been handled so ham-fistedly that it brings only sympathy and support for Mr Johnson'. The panel has the power to expel Johnson depending on the findings of the investigation. Attacking Boris merely helps the Opposition.
On Friday, the UK's equalities watchdog said Mr Johnson's remarks were "inflammatory and divisive" and his comments risked "vilifying Muslim women".
The founder of the Conservative Muslim Forum, Lord Sheikh, has written to Mr Lewis demanding "serious action", while former attorney general Dominic Grieve said he would quit the party if Mr Johnson became prime minister. However, Johnson has received some support, including from a a leading Imam and Blackadder star, Rowan Atkinson.
There were further signs of grassroots Tory anger over the affair, with the Telegraph giving over its whole letters page to reaction from readers after being "inundated" with messages of support for Mr Johnson.
Conservative sources have insisted that the probe into Mr Johnson's comments was triggered automatically after the receipt of a number of complaints.