More than 70 metres of cable had been cut from the railway near Elmswell station.
British Transport Police (BTP) detectives are appealing for information following the incident which was reported to BTP on Wednesday at 10.15am.
Investigators were called to the scene close to Elmswell station after engineers working on the line discovered the damage.
A full area search was carried out by BTP and Suffolk Constabulary officers who discovered the long lengths of cable had been cut and disturbed, although not taken.
Further enquiries with Suffolk Constabulary discovered that a grey Mitsubishi Shogun had been abandoned close to the scene on Monday, which detectives believe the offenders used to access the line.
No delays were caused to trains running through the area and the cable was removed by Network Rail engineers to be repaired.
BTP is appealing for anyone who may have seen suspicious activity in the area, or who may have seen a similar vehicle close to the tracks, to come forward.
Anyone with information is asked to contact BTP on 0800 405040 quoting incident number 148 of 30/10/2013. Information can also be passed to Crimestoppers anonymously on 0800 555111.
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