The simple answer is no: wake-on-lan is a BIOS feature intended to solve the problem of powering up the machine without having to have the machine on to process network traffic.
But if you have terminal access to the machine then you can easily shut it down, to sleep, suspend or hibernate. The technology to do this is called ACPI.
To hybernate/suspend, try http://linux.about.com/od/commands/l/blcmdl1_apm.htm
To hybernate/suspend for a certain amount of time, try apmsleep: http://linux.about.com/library/cmd/blcmdl1_apmsleep.htm
Personally, I would create a user called acpi on the machine you want to control, and give that user permissions to run apm and apmsleep using sudo.
For example, to use one machine to tell another to standby, you could then use:
ssh -f acpi@host sudo apm -S