In footage recorded by another passenger, David Lawrence, on the flight from Barcelona to Stansted, a man calls 77-year-old Delsie Gayle, who is disabled, an “ugly f****** c***” and an “ugly black b******”.
The budget airline reported the matter to Essex Police after video of the row was shared tens of thousands of times on Facebook.
On Tuesday, Essex Police said: “We have worked to identify both parties involved in this incident and passed this information to the Spanish authorities, who are leading on this investigation.
“Our officers will continue to provide assistance where necessary throughout the course of this case.”
The row took place before take-off on Friday afternoon.
At the beginning of the footage, the woman’s daughter can be heard telling the man her mother is disabled.
He replied: “I don’t care whether she’s f****** disabled or not – if I tell her to get out she gets out.”
He told staff to move the woman to another seat, adding: “If you don’t go to another seat I’ll push you to another seat.”
The man, who has not been named, shouts “don’t talk to me in a foreign language you stupid ugly cow”.
Mr Lawrence criticised fellow passengers for not intervening – though one man on the row behind was trying to stop the man from being abusive.
He said: “I looked around to see if there was going to be a response from the public, I didn’t hear any.
“I saw smirks and giggles going on.”
He added: “Eventually someone [a crew member] came down and moved the woman from her seat and placed her further back, leaving the man sitting by himself.”
A Ryanair spokesman told Sky News: “We have reported this to the police in Essex and as this is now a police matter, we cannot comment further.”