Does an FCC grant limit which antennas I can use with an FCC-certified module?

Sometimes explicitly, always implicitly. An FCC grant may or may not list specific approved antennas, antenna types, or maximum antenna gain values. When those details are listed on the grant, the limitations are explicit and binding. You must use only the approved antennas or stay within the stated gain and configuration limits. When those details are not listed, as is the case for many cellular and RF modules, it does not mean antenna choice is unrestricted. It means the FCC has approved the radio at the conducted output level and has shifted radiated compliance responsibility to the host product integrator.

In practice, antenna choice is constrained by RF exposure, spurious emissions, and overall system compliance in the final product. Changing the antenna type, gain, placement, or ground reference can materially affect the device's radiated characteristics. If those changes cause the final product to exceed RF exposure limits or alter emission behavior in a way that falls outside the original compliance basis, the module’s FCC certification no longer stands on its own. The integrator is then responsible for performing additional evaluation and, if necessary, updating the regulatory filing.

Even when an FCC grant does not specify antennas, it still limits antenna selection through the back door. The limits only appear in compliance math, not on the face of the grant.