Arlauskis, who played in the 6-0 rout at Real Madrid and up to halftime in Monday’s 5-0 home defeat by Real Sociedad before coming off, has a torn muscle in his right thigh.
Pau Lopez took his place against Sociedad.
"Arla will miss the first team's next matches after it was confirmed this morning the Lithuanian goalkeeper is suffering from a torn right adductor," the club said on their website (www.rcdespanyol.com).
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"He will be out for between three and four weeks."
Coach Constantin Galca's job came under review on Tuesday with Espanyol not having won in seven games since a 1-0 home victory over Las Palmas before Christmas.
Galca was expected to be sacked but the Barcelona-based sports daily El Mundo Deportivo said the four captains, Javi Lopez, Victor Sanchez, Victor Alvarez and Abraham, spoke up for the Romanian at a meeting and earned him a reprieve until at least the weekend.
Fourth from bottom Espanyol, one point above the relegation zone, travel to 14th-placed Valencia on Saturday.
Valencia coach Gary Neville is also under fire because his team have gone nine league matches without a victory.
(Reporting by Rex Gowar, editing by Ed Osmond)
