Footage posted on social media showed a plane passenger calling 77-year-old Delsie Gayle an "ugly black b******" and telling her "don't speak to me in a foreign language, you stupid ugly cow".
The incident took place on Ryanair flight FR015 at Barcelona Airport on October 19, before it left for London Stansted.
Essex Police said on Tuesday: "We have worked to identify both parties involved in this incident and passed the 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 woman who was subject to the abuse said she felt "very low" about the incident.
Speaking to ITV News, Mrs Gayle, from east London, said: "I feel very low. He pays his fare, I pay mine. So why did he abuse me for that? Because of the colour of my skin.
"If I had done that to him, I'm sure they would have called the police."
The three-day trip to Costa Brava had been planned by Ms Gayle's daughter to raise her mother's spirits as it is nearly one year since the death of her husband of more than 50 years.
Ms Gayle said her experience has discouraged her from flying with the low-cost airline in future.
She continued: "I feel really depressed about it. I go to bed and say: 'what have I done?'
"I haven't done anything to attack him, it's because of the colour of my skin I was abused like that.
"I decided I would not fly with that airline because they don't treat you with no respect."
Ryanair said on social media last Sunday they had reported the incident to Essex Police.
It added: "As this is now a police matter, we cannot comment further."
Her daughter, Carol, who was with her mother on the Barcelona flight, criticised Ryanair's response, and claimed they have not yet received an apology from the airline.
She told ITV News: "He should have been moved or taken off the plane and nothing was done.
"I know if that was a black person racially abusing an elderly woman the police would have been involved. It would have been a different matter.
"Nobody has apologised. We've not had nothing. We just want an open apology from Ryanair.
"I can't even watch the video any more, it's just so upsetting."