In a leaked letter, Mr Skates said he was informed this was because of the current level of investment.
He meets Network Rail officials on Thursday after describing conditions for rail passengers as "unacceptable".
Network Rail said it was committed to working with the Welsh Government to get value for taxpayers' money.
Mr Skates has accused the company - which maintains tracks across the UK - of a lack of investment in clearing leaves this autumn, which cause damage to train wheels because of the extra braking pressure required.
He believes this has led to over-crowding and reduced punctuality of services as it forces more rolling stock to be removed from routes.
Arriva Trains Wales said 54 out of its fleet of 127 have had to be taken away for repairs this autumn - an increase of 54% on the same period last year.
In the letter seen by BBC Wales, sent last month to Network Rail's route managing director Andy Thomas, Mr Skates said Arriva Trains Wales raised concerns about the level of work being carried out to clear leaves from the lines.
He wrote: "I have been informed that Network Rail responded that this was due to budgetary reasons and that at the current level of investment it would take 28 years to get the Welsh network up to the prescribed standard."
A Network Rail spokesman said: "We have jointly concluded with Arriva Trains Wales that the reduction in fleet availability cannot be solely related to Network Rail's autumn plan as we are increasing spend and activity.
"We are committed to working jointly with Arriva Trains Wales and the Welsh Government to ensure maximum value for taxpayers' money."
In a debate at the Senedd on Wednesday, Plaid Cymru's economy spokesman Adam Price described current conditions for Welsh rail passengers as a "national crisis".
He referred to three examples on social media yesterday in which one passenger told of his experience of a train catching fire, one had been on an overcrowded service where a passenger fainted, and another claimed to have a seat for the first time in 11 months.
An Arriva Trains Wales spokesman denied one of its trains had caught fire, instead saying there was a problem with an exhaust.
He said: "We understand and apologise for the frustrations around the capacity issues faced by commuters which has been made worse recently by the additional maintenance required on damaged train wheels caused by the autumn leaf-fall.
"We continue to work hard with our partners in Network Rail to reduce the impact of this issue."
Network Rail believes it will take 28 years to get the Welsh rail system up to standard, Economy Secretary Ken Skates has been told.