Two men and a woman were picked up from northern Rajasthan state following a tip-off from the police in neighbouring Haryana, where the blast took place.
The blasts and blaze on the cross-border train killed 68 people, most of them Pakistanis.
India has said it would share with Pakistan details of the investigation.
The three persons were detained by police from Bikaner, one of Rajasthan's four districts bordering Pakistan, says the BBC correspondent in the state.
Rajasthan Interior Minister Ghulab Chand Kataria told the BBC that the police had initially detained one person, who resembled the sketch of a man that the police put out on Tuesday.
The two others who had been picked up were relatives of the man, he said.
"It is too early to say anything until the interrogations are complete," the minister said.
The police are questioning the three, and no details are yet available.
It is not clear who was behind the attack on the Friendship Express near Panipat, 80km (50 miles) from Delhi, and no group has admitted carrying it out.
The police issued sketches of two men they believe got off the train just moments before it was hit by the deadly bombing on Sunday night.
The fire engulfed two carriages on the Samjhauta (Friendship) Express
However, it is not known how the two men got off the speeding train, which had only slowed down after the driver was alerted that there was fire in two carriages.
The police has said it has recovered 14 plastic bottles "filled with kerosene", a suitcase and plastic digital timers from the site of the blasts.
India and Pakistan have condemned the blasts and vowed to continue with the peace process.
The two countries established a joint panel last year to share intelligence to help fight terrorism.
Similar attacks in the past have been blamed by India on Pakistan-based militants.
The bombing of commuter trains in Mumbai last year effectively derailed peace talks for many months - although allegations of Pakistani involvement were never proved and vehemently rejected by Islamabad.
The twice-weekly cross-border Friendship Express - one of only two rail links between India and Pakistan - was restarted in 2004 after a two-year gap as part of the peace process.
Talks have been going on for three years, but have made little headway on key issues such as the dispute over Kashmir.
BBCGüncelleme Tarihi: 20 Eylül 2018, 18:16