Sir Nicholas Soames, who represents Mid Sussex, said he had spoken to Transport Secretary Patrick McLoughlin urging the measure.
He said: "There have been too many cases where passengers on the railway are treated extremely disrespectfully by staff simply not turning up."
A Southern Rail spokeswoman said there were "many reasons why this happens".
Sir Nicholas said: "Where the rail companies allow this to happen they should be fined for it, because I think if you consider how expensive it is to travel on the train it is a contract between the passenger and the rail operator.
"And it is one which the rail operator regularly breaks."
He added: "If you ask anyone who commutes or travels extensively on the train in the Southern region they will tell you it happens very regularly."
A Southern Rail spokeswoman said when services are disrupted it can lead to train crews being displaced and unable to crew their next scheduled service.
She said: "Sickness, annual leave, reliance on taxis and occasional rostering errors also all have an effect on the ability to crew every train every day.
"We are currently training new drivers, and as at the end of August, 60 new drivers had become qualified since the beginning of the year."
Rail companies should be fined for cancellations caused by staff "no shows", a Sussex MP has said.