A local army officer told one news agency that the man's niece was also killed.
Brigadier-General Rageb Al-Omeri said: "The bomber blew herself up as the sheikh came out of the house to meet her."
The US forces have been working with the Awakening Councils, units of armed Sunni residents who patrol their neighbourhoods.
Iraqi and US leaders have praised the neighbourhood units for their contribution to improved security.
A US military spokesman said recently there are now as many as 90,000 members of such units across Iraq.
Women have been involved in a number of recent bombings, including two large explosions in Baghdad markets in February that killed at least 99 people.
Attacks across Iraq are said to have fallen by 60 per cent since last June, when an extra 30,000 US troops became fully deployed.