Multicast Question - Does a router always need to be present to handle Multicast traffic?

I'm trying to learn about multicast protocol and all the material I can find alludes to IGMP running at the router level. My confusion is, multicast groups have a unique MAC address, derived from the IP range that's a part of the group.

With the above in mind, for a local network (e.g., all devices on a single switch and on the same VLAN) does the Router need to be involved? Can't the switch itself run IGMP and use the Layer 2 MAC address to forward multicast packets to appropriate recipients?