The man, who lives in Spain, was detained in the eastern town of Castellon, Interior Minister Juan Ignacio Zoido said in a Twitter message.
The 24-year-old man, who was detained in the eastern town of Castellon, was close to several members of the group, especially Abdelbaki Es Satty, a Moroccan imam believed to have radicalised the youths that carried out the attacks, it said in a statement.
He is believed to have helped the cell obtain the ingredients they used to make over 100 kilos (220 pounds) of the explosive TATP and provided them with vehicles to transport it.
"Various members of the cell counted on the help of the suspect, who at the very least, provided his personal identification documents which they used to buy hydrogen peroxide, a key ingredient to make TATP," it said.
"In addition, he provided the terrorists with methods of transportation used to move part of the explosives."
TATP has become the explosive of choice for the Islamic State (IS) group as it can easily be made from ingredients such as acetone and oxygenated water that are readily available in high street stores.
Investigators found 15 kilos of the explosive -- dubbed the "mother of Satan" -- in a flat near Brussels after suicide attacks in the Belgian capital in March 2016.
It was also used in the November 2015 attacks on Paris, and in a bombing that targeted concertgoers in Manchester in May.
In last month's attack, jihadists killed 16 people using vehicles and knives in a two-pronged attack in Barcelona and the seaside resort of Cambrils, with the bloodshed claimed by IS.
The main suspects were of Moroccan origin, although most had lived in Spain for several years.
Police shot dead six of the suspected members of the cell that carried out the attacks and arrested another four.
Two other suspects -- including Es Satty -- died in an explosion at a house used by the plotters at Alcanar, southwest of Barcelona, on August 16 on the eve of the Barcelona attack.
Police believe the explosion at the house prompted the surviving members of the cell to bring forward their attack plans, resulting in the vehicle rampages in Barcelona and Cambrils.