The Manchester Road shop is due to close before Christmas.
It will be the sixth Huddersfield post office to close since March.
After it shuts, people will have to use either Milnsbridge or Linthwaite post offices.
Customers have contacted Ms Mountford in a bid to keep the Cowlersley office open.
She said: "The two alternative post offices are not at all suitable.
"The Milnsbridge office is in the centre of a busy shopping area and parking is difficult.
"The Linthwaite office is more accessible, but is in the wrong direction for Cowlersley people. Their journeys tend to head east towards Huddersfield from that area."
The MP added: "It is pretty obvious to me that because the Post Office has to close 3,000 offices it is choosing them in an arbitrary fashion, according to the willingness of the postmistress or postmaster to retire or take redundancy, rather than according to local need or provision.
"Our only chance is to make it clear that we cannot afford to lose this vital service. I urge people to make their views known and write to the consultation team.
"They must understand the backdrop to any decision that they make."
The closures are part of Post Office Ltd's plans to restructure and modernise more than 9,000 urban branches.
It says that in many cities and towns there are too many outlets competing for too little business.
The Post Office says it is heavily in debt, but this is disputed by unions.
John Tracey, secretary of the Communication Workers' Union's Bradford branch, said: "They have exaggerated the debt. The Audit Commission has found it is not in as much debt as it says. It is a trick.
"They are not particularly bothered about the impact on customers," he added.
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