The number twos then move to the next partner every two minutes.
You will want to use a timer and a bell, buzzer, or some kind of sound to notify participants when the two minutes is up, so they don't have to time keep on top of participating in introductions.
The icebreaker is also not intimidating because the attendees—and they worry about this and ask if they will have to touch another attendee—are not put off by a quick handshake when they meet their next speed dating companion.
When your participants don’t know each other, ask them to number off by one and two; half of your participants become ones and the second half become twos.
Even your shyest or most uncomfortable participant can manage to talk with another person for two minutes.