My Nikon 105mm drops from f/2.8 to f/4.5 at closest focus, so that sounds right.
A post at betterfamilyphotos has a post where they say (emphasis mine):
You would imagine that using a macro lens is the same as using a
normal lens, and you would be right except that with a macro lens when
you get close to 1x magnification, you start losing light. My 60mm for
example starts losing light at close ranges until it reaches 2 stops
of light loss at 1x magnification, this means that the effective
aperture is f/5.6 instead of f/2.8 (regarding light quantity entering,
not DoF). If you are using auto modes on the camera like aperture
priority or using flash in TTL mode then the camera will auto
compensate for the light loss, but if you're metering light manually
you need to take it into account, Canon has included a table in the
user manual with the light loss values at each magnification level.
So if you have access to the manual for this lens, or request one from Canon, it should verify the information. It's expected for a close focusing macro to lose 1-2 stops.
The above post is incorrect, however, in saying that the reduction in aperture doesn't affect DOF. It does. Two references for those interested in the physics of it: