The man was arrested in the Sussex area on Saturday.
Scotland Yard said the 38-year-old was taken to a local police station and has since been released under investigation.
The force added that the arrest was not made in relation to events heard at the Grenfell Tower Inquiry this week.
A total of 72 people lost their lives as a result of a fire at the west London block of flats in June 2017.
The Grenfell Inquiry was ordered by former Prime Minister Theresa May the day after the horrific fire, with a promise it would “leave no stone unturned”. Divided into two phases, it would look respectively at events on the night of the fire, and longer-term causes in the period preceding.
Phase One, conducted between June and December 2018, published its results last October.
It found “significant systemic failings” on the part of the London Fire Brigade, which maintained a “Stay Put” order, keeping residents in their apartments long after they should have been evacuated.
A public inquiry, chaired by Sir Martin Moore-Bick, examining the circumstances and causes of the disaster, is ongoing.