I have an instance of Solr, hosted with Tomcat that recently started creating minidump files. There are no errors in any of logs, and Solr continues to work with out a hitch.
This article has decent information on both Linux and Windows JVM dump files. Have yet to test it myself on my current version of Java 7....
From that site:
Disabling Text dump Files
If you suspect problems with the creation of text dump files you can turn off the text dump file by using the option: -XXnoJrDump.
Disabling the Binary Crash Files
You can turn off the binary crash file by using the option: -XXdumpSize:none.