He is apparently 16, was arrested in West London, and has been released on bail.
On Monday, a teenage boy aged 15 was arrested in County Antrim, Northern Ireland, on suspicion of offences relating to the Computer Misuse Act. He has also since been bailed.
TalkTalk announced last week that it had been hacked, and that millions of customers' personal details may have been stolen.
TalkTalk says it has received a ransom note from someone claiming to be the hacker following the attack, which reportedly demanded £80,000 in bitcoin.
The company said on its website customer bank details and personal information may have been accessed in the attack, but sensitive financial information had been protected. TalkTalk also said it will only waive contract termination fees for customers that have money stolen from them following the hack.