National Rail tweeted about the incident - understood to be in the Leominster area - just after 3pm on Sunday and say it affects Transport for Wales routes through Shropshire to Manchester and Holyhead and West Midlands Railway between Hereford and Birmingham New Street.
Great Western Railway between Hereford and London Paddington is also affected.
A spokesperson for Network Rail said: "A person has been hit by a train in the Hereford area. Whilst the emergency services carry out their work all lines will be closed.
"Services will be cancelled, delayed or revised."
Disruption is expected until 6pm.
Transport for Wales says tickets may be used on Cross Country Routes between Cardiff Central / Bristol Parkway and Manchester Piccadilly.