The former One Direction singer, 25, was with girlfriend Eleanor Calder at the arrivals gate of the airport when the incident happened, the Press Association reports.
The couple had returned to Los Angeles after a holiday in Las Vegas.
A source said the photographer made a citizen's arrest on Tomlinson. Calder is also thought to have got involved in an argument with onlookers who began filming the row.
Tomlinson's lawyer Martin Singer said: "The paparazzi provoked and caused the altercation that occurred with Louis at the airport this morning.
"This is not the first or last time that a paparazzi has created an altercation with a celebrity.
"While the altercation was going on with the paparazzi, three other individuals were attacking his girlfriend during this incident and he came to her defence."
Tomlinson is currently releasing solo material while One Direction are on hiatus.
A source said he did not have to pay the £16,000 ($20,000) bail, as he was released under 'own recognisance' in which an individual pledges in writing to appear in all court proceedings.
A court date was set for March 29, said reports.
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