The proposals, put forward by the king himself last month in a rare address to the nation, would hand greater power to the prime minister and parliament. The king would remain at the helm of the army, religious authorities and the judiciary.
They follow pro-democracy protests inspired by this year's uprisings around the Arab world.
Forty-thousand polling booths across Morocco opened at 8am local time, with early results expected late Friday or early Saturday. About 13 million of the country's 32 million people are registered to vote.
Although King Mohammed is widely expected to win, Morocco's February 20th Movement said the proposals didn't go far enough, and called for a vote boycott. The group has rallied support for several demonstrations through social media websites.
In a statement posted on its Facebook page on Friday, it said: “We are calling for a boycott of this referendum because the constitution it proposes consecrates absolutism and will not make corruption disappear.”
By midday on Friday, Morocco's Interior Ministry told the state news agency Maghreb Arabe Presse that voter turnout was at 26 percent, and that the king had cast his vote in front of supporters in Rabat.
The BBC reported that low voter turnout at the referendum could spur demand for even greater freedoms – while adding that main political parties, unions and religious leaders have been urging support for the new constitution.
The reforms have received interational approval, with the European Union describing them as “a clear commitment to democracy”.
The vote will be the first constitutional referendum under the king's 12-year rule, and follows parliamentary polls in 2007, at which voter turnout stood at a record low of of 37 percent.