George Freeman said he was left "stranded for an hour" because the 9.09am Greater Anglia service from Cambridge to Attleborough this morning was not held up for him.
The Tory MP described how he was one of five passengers who "sprinted" along the platform after a connecting service from London King's Cross was delayed.
He expressed his frustration in a series of tweets to Greater Anglia, stating that the member of staff responsible for dispatching trains could see them running but chose to close the doors and instruct the driver to depart.
The worker then "smirked and ignored us", the MP for Mid Norfolk added. Greater Anglia replied that "in most cases" it cannot hold trains when services run by other operators are late.
Mr Freeman responded: "Not even for 15 seconds when passengers from a connection are AT THE DOOR?!" The company apologised and accepted "there should have been some discretion".
Responding on Twitter, shadow transport minister and York Central MP Rachael Maskell wrote: "Over the last year 10,000s of passengers have been left stranded at stations, due to this Government’s failures. I hope he spent his time, reflecting how he will end #railfail."
The MP said it was a "huge honour" when he was appointed as a transport minister by Prime Minister Boris Johnson last month.
He joined as part of a reshuffle which saw Harrogate MP Andrew Jones lose his job as Rail Minister. His portfolio includes technology, innovation, decarbonisation and connectivity.