"Just equipping long-distance trains isn't enough, regional trains and S-Bahns should have wireless internet access too", he told the Süddeutsche Zeitung (SZ).
He added that the state-owned rail operator should offer passengers access for no extra charge.
DB and its competitors in the regional market should "adjust to people's changing ways of life and offer mobile access and high-speed internet in all trains", Dobrindt said.
As of January, first-class passengers in DB intercity (ICE) services can connect to on-board Wi-Fi for free, however second class passengers will have to wait until 2016 to get their own access.
The rail operator says it needs to wait for the technology to work reliably before outfitting entire trains.
Responding to the SZ, DB said that it operated regional trains on behalf of each state, unlike long-distance traffic.
"If people want wi-fi in regional trains, the necessary on-board technology has to be provided for in the transport contract", the company told the newspaper.
"Desperately needed mobile network infrastructure has to be available along the whole length of the line.
"If such an order is made, we'll gladly equip our trains."
SEE ALSO: Free train wifi on track for 2016