"We have been informed that 10 of our employees from the voting stations in Jazirah and Khalidiyah were kidnapped," an election official told reporters on Saturday.
An AFP correspondent in the region quoted witnesses as saying armed men seized the workers as they headed to the vote stations they were to staff.
The referendum, which went off quietly elsewhere in Iraq, ran into a few problems in al-Anbar, where Sunni Arabs opposed the draft charter.
According to the commission, 60 voting stations of a total of 207 in the province did not open for security reasons.
In general, however, the vote was spared problems that marked general elections on 30 January, during which 36 people had died.