The 23-year-old man was arrested in a bar in the northern Pigalle area of the city at 6.30pm on Tuesday evening, according to newspaper Le Figaro.
The story of Rajinder Singh, who went by the nickname Babu, has stirred up much emotion and sympathy in France. He died after going to the aid of a woman who was being mugged on a metro train on Thursday evening.
After continuing a scuffle with the attacker on the platform at the Crimée station in the north of the city he was either pushed or fell onto the tracks and was electrocuted, dying instantly.
Police used video surveillance footage to help identify the man. According to the newspaper, the man of Egyptian origin fled the scene of the death but returned shortly afterwards, showing his face to cameras.
The dead man was originally from the Punjab state of India and came to Paris seven years ago to earn money to help his family. He had been working as a pizza deliverer and had moved into an apartment with his girlfriend.
A moving tribute to Rajinder Singh in Wednesday's Le Parisien newspaper prompted hundreds of supportive comments on the newspaper's website and its Facebook page.
"This man died simply because he put himself between a victim and a mugger," said one. "If we all had the same values, Babu wouldn't be dead."
The newspaper also reported that Mr Singh's family in India was desperate for his body to be sent home for a traditional funeral, but that friends were struggling to get the €5,000 ($6,600) required for the journey. The charitable foundation of the Paris transport network, Fondation RATP, has stepped in and will cover the costs.
"The president of RATP, Pierre Mongin, has been very touched by this drama and would like us to cover all repatriation costs," said Florence Rodet, head of the foundation.