The 22-year-old Englishman travelled back to his parent club for diagnosis after Saturday's 1-1 draw with Inverness Caledonian Thistle.
"Unfortunately I have torn my ac joint in my shoulder," he said on Twitter.
"Which is going to keep me out for around two to three months. Gutted I won't be involved in upcoming games."
Matthews joined Accies on a season-long loan from the English Championship club and has made 13 appearances.
Accies sit in ninth place in the Scottish Premiership, two points ahead of bottom side Partick Thistle.
Matthews went off eight minutes before the end of the game against Caley Thistle and was replaced with 23-year-old Robbie Thomson, Accies' summer signing from Queen of the South.
On-loan Norwich City goalkeeper Remi Matthews will be sidelined for up to three months after an injury picked up with Hamilton Academical.