The so-far unnamed person was hit by a train between Moorgate and Finsbury Park, Thameslink tweeted. Their condition is not currently known.
Thameslink added: "All lines are blocked between these stations whilst the emergency services work to deal with this incident."
Others reported seeing emergency services rush to the scene.
Writer and presenter Nicky Woolf tweeted: Anyone know what's going on at Highbury and Islington station?
"It's been evacuated for half an hour and there are like 15 emergency vehicles outside it."
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Thameslink
National Rail also warned travellers to expect delays.
It said that the line was expected to be closed until at least 9.30pm.
A post on its Twitter account said: "The emergency services dealing with an incident near the railway between Moorgate and Finsbury Park. Whilst they do their work trains all lines are blocked.
"Trains running between these stations may be cancelled, revised or diverted via London Kings Cross."
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Thameslink confirmed that trains will not be calling at Moorgate, Old Street, Essex Road, Highbury & Islington and Drayton Park.
It said that travellers can use their tickets on another service on Thameslink and Great Northern trains on any reasonable route to get to their destinations.
They can also use the London Underground and Transport for London buses.
While the condition of the person remained unclear, many social media users quickly shared their hopes that they were OK/
Sleeper Train wrote: "Sorry to hear this."
johfam tweeted: "Something about Finsbury Park makes me extremely uncomfortable and sad."
Express.co.uk has contacted the British Transport Police for further details.