The 35,000 sq ft store and car park is being built on land above the tunnel, after Tesco received approval to build on the site in 2002.
Tonnes of rubble from the tunnel, which is used by Chiltern Railways connecting Birmingham with London Marylebone, fell onto the line yesterday evening.
No one was injured in the collapse but the British Transport Police said that the line would remain blocked for at least two days.
A Tesco spokesman said: "Following last night's tunnel collapse at the site of our Gerrard's Cross development Network Rail and the project's civil engineers, Jacksons, are investigating the cause and working round the clock to get trains running again.
"Thankfully nobody was hurt and whilst the experts on the ground are rightly running the incident we are helping in any way we can."
Local residents have campaigned against the building of the store in their town for some years, amid concerns that it would have a negative effect on local traders.