The letter to Matt Hancock said that some practices were waiting 'up to a month' for additional vaccines to be delivered, which 'raises concerns that there are significant distribution problems'.
Professor Marshall's letter said that it was 'crucial that the government are as transparent as possible about any shortages that may occur, so that GPs can make appropriate planning decisions'.
'It will not be helpful for practices or acceptable to patients if current claims that there are no supply problems are exposed as overly-optimistic in coming months,' the RCGP chair added.
'I hope you can provide me with some assurance that there is sufficient supply of the vaccine and that any distributions problems will be communicated to GPs as a matter of urgency.'
The letter comes after Professor Marshall highlighted problems around flu jab shortages last week. His warning came as a GPonline poll found just one in four GPs were confident their practice would have enough doses of flu vaccine to meet demand.
Flu jab shortages
The government has repeatedly said that there will be enough supply of the flu vaccine to meet demand this winter. However many practices have seen high levels of uptake this year, raising concerns that there could be shortage.
In a Commons debate last week Mr Hancock insisted that sufficient supplies were available.
'There are enough for everybody in a priority group who needs them,' Mr Hancock said. 'I stress that this is a roll-out: nobody needs to have a flu jab before the start of December, but people can have it in September or October and it will then cover them for the winter, so we are rolling this out and more appointments will become available in good time.
'We have 30m jabs in total, more than we have ever had before and almost double what we typically have had in the past, and those are available. I am really glad to say that record numbers of people are coming forward to get flu jabs, and I welcome that.'
Professor Marshall's letter highlighted that GP practices were working hard to vaccinate those in traditional 'at risk' groups. However, he added that the college was 'increasingly concerned with reports from practices, pharmacies and patient groups that suggest there is an issue with supply of flu vaccines'.
Expanded flu campaign
Last month high street pharmacist Boots said that it had suspended 'any new bookings for our private and NHS under-65s flu vaccination services'. It said the move was necessary 'due to the level of demand and limited stock that we have available'.
At present GP practices are only able to vaccination patients aged over 65 and other patients in the eligible at-risk group. The government has said that it intends to roll out flu jabs to all over-50s this year, but practices have received little detail on plans for vaccinating this expanded cohort.
This year's DES made clear that the government would only begin vaccinating this group once at-risk groups had received the jab and subject to vaccine supplies. Vaccine supplies for the over-50s cohort are expected to be supplied by the DHSC from central stocks.
A DHSC spokesperson said 'There is no national shortage of the flu vaccine, with enough doses for 30 million people to be vaccinated in England.
'The vaccine is already being delivered for those in at-risk groups, including the over-65s and this will continue throughout the winter months, so there is still time for those eligible people to get their vaccinations.'