The Brazilian had to be replaced after just 17 minutes as Barca ran out 4-1 winners at Granada on Sunday with a slight tear to the inner meniscus of his right knee.
"How it evolves in the next 48 hours will determine the choice of treatment," Barcelona said in a statement.
Barca boss Luis Enrique is hopeful the South American will not miss his side's Champions League quarter-final clashes with Juventus.
"It doesn't seem like it is very serious, but it is something that will mean he misses the next few weeks," said Enrique.
"He will be a big miss."
Rafinha had become a key player in Enrique's switch to a 3-4-3 formation following a 4-0 thrashing by Paris Saint-Germain in the first leg of their Champions League last 16 tie.
However, he has an unfortunate history of knee injuries having missed the majority of last season to cruciate ligament damage.
Barca face a huge month in their bid for a second treble in three years.
As well as facing Juventus on April 11 and 19, they travel to La Liga leaders Real Madrid on April 23.