EMR said pre-planned engineering work meant all lines between Bedford and London St Pancras were already closed on Saturday and Sunday.
It added that from Monday to Thursday, one train per hour would run between Sheffield and Bedford, Nottingham and Bedford, and Kettering and Corby, but there would be no services south of Bedford.
Network Rail’s East Midlands route director, Mark Budden, said: “We know passengers will want to understand when services can resume.
“We will provide updates as soon as we have a clearer understanding of the recovery work required and when the railway can safely reopen.”
Ellie Burrows, Network Rail Eastern regional managing director, added: “This is a complex and challenging task, and our teams will be working tirelessly to reopen the railway so we can resume services between Bedford and London.
“While investigations are still at an early stage, current indications are that this was a tragic, isolated incident.”