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.
Just plain
UPDATED:
At least on Debianish systems, meteor installs its own copy of node in /usr/lib/meteor/bin, so node -v
should tell you./usr/lib/meteor/bin/node -v
should tell you. If it's not there, it might be in /usr/local/lib...
On my Debian system, the version is 0.6.17.
Another way is to check the History.md file on the github project. While I'm wiriting this answer, the last update was on meteor 0.5.5, where they updated node.js to v0.8.18.
You can use mnode, but it seems it doesn't work with meteor 0.9. I also recommend reading this Arunoda article. It has an alternative approach at the end.