A signalling system at Diss has been damaged, resulting in Greater Anglia services between Norwich and London being cancelled.
Services from Norwich to Cambridge and Norwich to Sheringham have also been suspended or delayed.
The rail company is advising passengers of alternative travel options and of its delay repay policy.
Greater Anglia said disruption on the Norwich to London Liverpool Street line is expected until 21:00 BST.
It said services are unable to depart from Norwich towards Diss and Ipswich and from Diss towards Norwich whilst Network Rail engineers examine the line.
There are currently no replacement bus services available to run between Norwich and Diss, it said.
Greater Anglia has apologised for any inconvenience caused.
All lines were blocks on the Norwich to Cambridge line after lightning struck between Attleborough and Ely.
Disruption is expected until the end of the day.
Greater Anglia said Network Rail staff are on site and are repairing the signalling system however there is currently no estimate for the line re-opening
East Midlands trains services between Norwich and Liverpool Lime St are also affected.
Lightning strikes on rail routes through East Anglia have sparked travel chaos.