I have installed meteor under linux, and I don't really know which version of node.js meteor is using.
Answer for MacOS and Meteor > v1.1
The node binary resides in the dev_bundle of the meteor-tool:
~/.meteor/packages/meteor-tool/1.1.3/mt-os.osx.x86_64/dev_bundle/bin
$ cd ~/.meteor/packages/meteor-tool/1.1.3/mt-os.osx.x86_64/dev_bundle/bin
$ ./node -v
v0.10.36
Note: The meteor-tool version does not match the version of Meteor, but in 99% of the cases you can assume that the latest version is used for your current Meteor.
At least in Meteor >= 1.5 you can also directly access the NodeJS bundled with Meteor and find out the version:
meteor node -v
Credits to Mickael for pointing that out.
I just typed meteor node -v while in a meteor application and got v0.10.43 back on the CLI.
When I just type node -v I get v5.5.0 as a return value.