Malcolm Shabazz, 29, succumbed in hospital to multiple injuries he suffered on Thursday.
Mexico's attorney general's office said an investigation into the incident was under way.
The US state department said that it was in contact with the family and offering appropriate assistance.
Shabazz was discovered with fatal wounds at Plaza Garibaldi, a popular tourist area packed with bars and restaurants, in the early hours of Thursday, officials said.
Miguel Suarez, a union activist who was travelling with Shabazz, said they had been in the country as part of their efforts to advocate more rights for Mexican construction workers in the US.
Mr Suarez said he and Shabazz were invited to a bar on Wednesday night by a woman.
The bar owner later demanded they pay $1,200 (Â£780) for drinks and female companionship, according to Mr Suarez.
He said that he escaped as a fight broke out, before returning to find Shabazz seriously injured on the ground outside the bar.
Mr Suarez said he took Shabazz to a hospital where he died of "blunt-force injuries".
Shabazz was the son of one of Malcolm X's six daughters,  Qubilah Shabazz.
When he was 12, he was involved in a fire that killed his grandmother Betty Shabazz, the widow of Malcolm X.
He was convicted of manslaughter and arson and sentenced to time in a juvenile detention centre.
Malcolm X, a black power activist and prominent figure in the militant Nation of Islam movement, was shot dead at a political rally in New York on 21 February 1965.
The grandson of US political activist Malcolm X has died in Mexico City following a fight in a bar, say Mexican officials.