It is a common misunderstanding that MUTAH wasn’t forbidden by Prophet Muhammad [SallAllah-u-Alaihi-wa-Sallam] rather it was Hadrat Omar [RadiAllahu Tala Anho] who forbade it. I am quoting three hadiths from many to prove this misconception wrong.
Book 008, Number 3263:

Ali b. Abi Talib [RadiAllahu Tala Anho] reported that Allah’s Messenger (SallAllah-u-Alaihi-wa-Sallam) prohibited on the Day of Khaibar the contracting of temporary marriage with women and the eating of the flesh of city’s asses.
[Sahih Muslim]
Book 008, Number 3266:

Ali (RadiAllahu Tala Anho) heard that Ibn Abbas (RadiAllahu Tala Anho) gave some relaxation in connection with the contracting of temporary marriage, whereupon he said: Don’t be hasty (in your religious verdict), Ibn Abbas, for Allah’s Messenger (SallAllah-u-Alaihi-wa-Sallam) on the Day of Khaibar prohibited for ever the doing of it-And eating of the flesh of city ‘s asses.
[Sahih Muslim]
Book 008, Number 3267:

Ali (RadiAllahu Tala Anho) said to Ibn Abbas (RadiAllahu Tala Anho) that Allah’s Messenger (SallAllah-u-Alaihi-wa-Sallam) on the Day of Khaibar forbade forever the contracting of temporary marriage and the eating of the flesh of city’s asses.
[Sahih Muslim]