Both players were in doubt for Saturday's La Liga game at home to Granada, the Spanish champions said on their website (www.fcbarcelona.com).
Xavi had a problem with his left hamstring, while Tello had damaged ligaments in his right ankle, they added.
Barca are already missing World Player of the Year Lionel Messi, who was ruled out for up to eight weeks after tearing a leg muscle in this month's 4-1 La Liga win at Real Betis.
Defenders Gerard Pique and Jordi Alba worked apart from their team mates on Tuesday as they continued their recoveries, Barca said, without specifying whether they would be available for Saturday's game at the Nou Camp.
Midfielder Cesc Fabregas, who could replace Xavi in central midfield against eighth-placed Granada, again trained normally as he works his way back from a knee problem picked up in the Betis game.
Unbeaten Barca top La Liga by three points from Atletico Madrid after 13 matches, with Real Madrid a further three points adrift in third.
Atletico are at home to Getafe on Saturday, when Real play at promoted Almeria.
(This story was fixed to correct Tello injury to ankle from knee)
(Reporting by Iain Rogers, editing by Clare Fallon)
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