The fire was first reported shortly after 4pm, and delays are now expected until at least 6pm.
Where possible, trains will be diverted between Sheffield and Leeds and will not call at Wakefield Westgate.
National Rail said: “You may use your ticket on Northern services on any reasonable route. CrossCountry customers may use tickets on TransPennine Express services on any reasonable route.”
Emergency services and National Rail staff are on site, but it is not yet clear when normal service will be able to resume.
Updates are being posted on Twitter using the hashtag #WakefieldWestgate.
More to follow.