The explosive device went off around 5.30am (0230 GMT) on Sunday under the first car of the train as it headed to the regional capital, Makhachkala, from the northwestern town of Khasavyurt, said Akhmed Magomayev, deputy chief of the region's railway police department.
The train car derailed and a crater was left in the track bed.
A woman who was among five people injured died on the way to a hospital, Magomayev said. One of the injured was a transport policeman on the train, he added.
State-run Rossiya television showed footage of the damaged train, its interior a jumble of battered wooden benches and torn ceiling panels.
The authorities were trying to determine the strength of the bomb, which was apparently set off by remote control, about 10km from Khasavyurt, Magomayev said.
Dagestan, which borders war-ravaged Chechnya, has been plagued by increasing violence believed to be connected with insurgents and criminal gangs.
The number of insurgent attacks in the region has more than doubled this year to 70, a Russian human rights group said last week.
Russian President Vladimir Putin,
(C), visited the area a week ago
Many of the recent attacks in Dagestan have targeted law enforcement officers or government officials.
Among those killed in the violence were the deputy interior minister, the nationalities minister and other officials from the multi-ethnic, mostly Muslim republic.
President Vladimir Putin visited Dagestan a week ago, a sign of Kremlin concern over increasing conflict in regions surrounding Chechnya.
Also on Sunday, police found two unexploded bombs in a car in the southern city of Kaspiisk, and engineers were working to defuse the devices, the Interfax news agency reported.