Ethnic parties were protesting proposals for a new province for the Urdu-speaking Mohajir urban majority, the BBC said.
The British broadcaster said two journalists were among those wounded.
Dawn News reported the rally was organized by members and workers of Awami Tehrik Party.
Police officer Mohammed Amir said the identity of the attackers remained unknown.
About a dozen vehicles and several shops were set ablaze.
Since the beginning of this year, hundreds of people have been killed in Karachi in the southern Sindh province, the BBC said.
Tuesday's rally came in response to demands for a separate province for the Mohajir ethnic group, which dominates much of urban Sindh, including Karachi, through the Muttahida Qaumi Movement, the BBC said.
Ethnic Sindhis have warned efforts to divide the southern province of Sindh could lead to widespread violence.
Wisconsin business offering 'therapeutic cuddling' forced to close
Costly malfunction causes beer flood at Boston-area brewery