Team doctor Cuno Wetzel told Swiss television that the Argentine, whose condition was stable, had suffered a severe concussion and broken nose after colliding with team mate Francois Affolter during the 2-2 draw against FC Basel.
"It's difficult to say how long the recovery will take, usually this type of injury needs several weeks," said Wetzel.
"The Argentine is on the road to recovery," added the club's website.
"We've seen that there are more important things than just victory or defeat," said FC Basel striker Marco Streller.
Basel coach Thorsten Fink added: "The result is secondary. The important thing is that Dudar gets better."
Dudar's journeyman career has been typical of many lesser-known South American players and far from the glamour enjoyed by the big names.
