Five other people were wounded in the afternoon blast, Mahmud al-Wazan, a colonel in the police force, told AFP. He said the victims appeared to be civilians.
Doctor Ahmad al-Ani from Ramadi hospital confirmed the casualty toll.
Wazan said the blast destroyed the Albu Faraj bridge on the Euphrates, in a northern district of Ramadi, which lies about 100 kilometres (60 miles) west of Baghdad.
"It is the fourth Ramadi bridge to get blown up and it was the last one civilians could use," he said.
The Sunni province of Anbar is a stronghold for the IS fighters who launched a major offensive across northern and western Iraq three months ago.