Orlandi had only just returned after a month on the sidelines with his left thigh, and has now injured the other.
"I'm gutted - I'm going to have to start all the rehabilitation work again," said Orlandi.
"It's back in the gym and on the bike, which is the most boring thing in the world.
"It's a bad feeling, but that's football. I've just got to get over it and try and get back as soon as I can.''
Spaniard Orlandi has been a regular for the Championship play-off chasers before picking up his first injury in the 1-0 win over Reading on New Year's Day.
Swans boss Brendan Rodgers has plenty of midfield cover with Joe Allen, Darren Pratley, Leon Britton, Mark Gower and Kemy Agustien all fit.
"It's disappointing news for us because he's a good player and he did well on Saturday having been asked to play in a different position," said boss Brendan Rodgers.
"But unfortunately the scan has shown a grade two strain which has ruled him out of the next period of games."
Source: BBC Sport
Source: BBC Sport