Disagreements between secessionist parties, which gained a majority in September's regional polls, have blocked the formation of a Catalan government.
Mr Mas said he supported the mayor of the Girona region, Carles Puigdemont, as his replacement.
Mr Mas has been in power since 2010.
In September elections, his Junts pel Si (Together for Yes) alliance won 62 of the 135 seats in the Catalan assembly.
But a small anti-capitalist and pro-independence party, the CUP (Popular Unity Candidacy), which holds 10 seats, has refused to support Mr Mas as leader.
"I am stepping aside and will not be standing as a Junts pel Si candidate for the re-election of president of the regional government," Mr Mas told a news conference in Barcelona.
Nationally, Spain faces weeks of political uncertainty after an inconclusive general election on 20 December.
In November the Catalan parliament voted to start the secession process - a move declared unconstitutional by Spain's conservative Popular Party (PP), which ran the country before last month's election.
Catalonia is a highly industrialised and populous region in Spain's north-east that accounts for about a fifth of the country's economic output.
Both the PP and the Socialists (PSOE), who came first and second respectively in Spain's general election, oppose Catalan secession.
Catalonia's acting leader Artur Mas has said he will step down as the pro-independence head of the Spanish region, to avoid triggering new elections.