James Duddridge tabled the motion on Thursday afternoon, having previously told HuffPost UK that Bercow “overstepped the mark” with his comments.
Bercow said he would oppose Trump addressing both houses of parliament if he made a state to visit to Britain, in an unprecedented attack from the normally neutral speaker.
Bercow said on Monday: “I feel very strongly that our opposition to racism and to sexism and our support for equality before the law and an independent judiciary are hugely important considerations in the House of Commons.”
Duddridge said the comments were “wholly inappropriate”.
Duddridge wrote to Theresa May earlier in the week asking if she would give ministers a free vote if a motion of no confidence were tabled.
Before he tabled the motion, he told HuffPost UK: “The Speaker has lost the confidence of the House. He overstepped the mark.
“He is not there to put forward his views, when he starts doing that he becomes incapable of representing the full opinions of the House of Commons.”
Bercow later said he was “honestly and honourably seeking to discharge my responsibilities to the House”.
Duddridge tabled the motion just before the February recess, meaning parliament will not be able to vote on it until MPs return on February 20.