Philippe Coutinho came close with a long range effort which was tipped wide by Vicente Guaita, with the Getafe goalkeeper also blocking a Yerry Mina header and a late effort from Luis Suarez.
Barca talisman Lionel Messi was below his best and off-target with various set-pieces, while Ousmane Dembele returned from injury but could not help from the Nou Camp bench.
After second-placed Atletico Madrid won at Malaga on Saturday, Barca's draw means Diego Simeone's side have eaten into their lead by two points.
Barcelona coach Ernesto Valverde was forced to play full back Lucas Digne in the centre of defence, alongside January signing Mina, making his full debut, due to injuries to Gerard Pique and Thomas Vermaelen, and Samuel Umtiti's suspension.
However the makeshift pairing was relatively solid, with Getafe creating few chances, the best of which saw Mina block Angel Rodriguez's shot after the forward broke through.
"It's good news for us that these two players did quite well in a difficult role," said Valverde.
"We would have liked to have taken the three points, (but) we're coming from a tiring month and logic says you can't win all the games.
"You can think that it's a slip-up, we have to keep moving forward, but this is not something that can't happen to you."
Barcelona failed to record a shot on target in the first half, something which has not happened since 2012, as they showed signs of tiredness after Thursday's King's Cup semi-final win at Valencia.
Suarez volleyed in just before halftime but was correctly ruled offside, with the Uruguayan ranting furiously at the assistant referee in frustration.
Towering defender Mina came close with two headers, one stopped by Guaita and another which flew inches past the post, as Barcelona failed to break down the visitors.
