Busquets was caught late by Tomas Pina in the 3-1 Copa del Rey success at El Madrigal and was subsequently confirmed to have damaged ligaments in his right ankle.
Tests on Thursday confirmed the Spain international will miss Sunday's league fixture, with a return date not yet confirmed, ahead of crucial games against Manchester City and Real Madrid this month.
A Barca statement read: "Club doctors confirmed that Sergi Busquets' ankle injury picked up in the game against Villarreal on Wednesday will rule him out of this Sunday's league clash with Rayo at the Camp Nou.
"His availability beyond that will be carefully monitored."
Pina was later sent off for another poor challenge, this time a second-half tackle on Neymar.
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