The flags at the end of the platform at the Astley Green attraction were damaged and others smashed then the intruders wedged a lump of concrete between the points on the line.
A museum spokesperson said: “This could have caused a serious derailment of our engine had it not been noticed beforehand.
"This is just the latest episode and should this vandalism continue we will have no alternative but to close off the site completely to walkers by securing the gates completely at both ends of the site.
"This is not something we want to do, but these stupid acts of vandalism need to be stopped before someone gets injured.
"We can’t run CCTV to that end of the site as we have no electric to the far side.
"We are looking at getting some installed, but again cost is prohibitive.”