The 30-year-old Samoa international forward was hurt in yesterday's pre-season friendly against Wakefield Trinity.
Masoe joined the UK side from NRL club St George Illawarra Dragons in 2017.
Hull said he is "awake and alert" after having overnight surgery in Leeds.
"Mose has an overwhelmingly positive mindset and would like to thank everyone for their concern and well wishes," said a club statement.
"He would also like to extend special thanks to staff at Leeds General Infirmary for their unbelievable care.