Hundreds of Buddhists took to the streets following the passage of a law that would allow temporary residents who hold "white papers" to vote.
More than one million Rohingya live in Myanmar, but they are not regarded as citizens by the government.
In 2012, violence between Muslims and Buddhists left more than 200 dead.
The clashes broke out in Rakhine province and sparked religious attacks across the country.
The so-called white papers were introduced in 2010 by the former military junta to allow the Rohingya and other minorities to vote in a general election.
Thein Sein had originally persuaded parliament to grant white-paper holders the vote, but later apparently changed his mind.
The announcement came just hours after demonstrations in Yangon. Those protesting resent what they see as the integration of non-citizens into the country.
"White card holders are not citizens and those who are non-citizens don't have the right to vote in other countries," said Shin Thumana, a Buddhist monk who took part in the protest.
"This is just a ploy by politicians to win votes."
However, Rohingya MP Shwe Maung, whose constituency is in Rakhine, argued that voting rights had only become an issue following the violence in 2012.
Buddhist monks are at the forefront of protests against Muslims. One high-profile leader is monk Ashin Wirathu, who recently used abusive language to describe the UN's special envoy to Myanmar.
In December, the UN passed a resolution urging Myanmar (formerly known as Burma) to give access to citizenship for the Rohingya, many of whom are classed as stateless.
Rohingya Muslims will not be able to vote in Myanmar's referendum after President Thein Sein withdrew temporary voting rights following protests.