The force said the man was arrested in the Sussex area on Saturday. He is the first to be arrested in connection with the fire.
He was taken to a local police station and has since been released under investigation.
The arrest was not made in relation to events heard at the Grenfell Tower inquiry last week, police said.
A total of 72 people lost their lives as a result of a fire at the west London block of flats in June 2017.
A public inquiry, chaired by Sir Martin Moore-Bick, examining the circumstances and causes of the disaster, is ongoing. Police had said they would not make any arrests until after the inquiry had concluded.
Grenfell survivors and supporters joined together for a virtual memorial in June to mark the third anniversary of the disaster.
Last week, in a matter unrelated to Saturday’s arrest, Scotland Yard said it would seek to "assess whether a criminal offence may have been committed" after a project manager on the Grenfell Tower refurbishment admitted "binning" her notebooks despite knowing a public inquiry and police investigation were under way.
Claire Williams, who worked for Grenfell landlords the Kensington and Chelsea Tenant Management Organisation (TMO), said she got rid of her records when she cleared her desk and left her job in May 2018, almost a year after the fire.
She told the inquiry: "There was nothing underhand about it. I was clearing my desk, I looked and decided that everything that was in there was formally represented in minutes or other paperwork and it was of little value.
"It wasn't a conscious, hiding anything decision, it was 'I'm clearing my desk'. I put them in the bin."