The world number one was beaten in three sets by Italy’s Jannik Sinner in his second group stage match at the ATP Finals in Turin.
Stefanos Tsitsipas withdrew from the tournament when he was 2-1 down to Holger Rune in the first set.
Alcaraz faces Andrey Rublev this afternoon, before Daniil Medvedev takes on Alexander Zverev tonight.
Two British players also meet in the doubles – with Neal Skupski partnering Dutchman Wesley Koolhof against Joe Salisbury and the USA’s Rajeev Ram.
