The announcement by Indonesian President Joko Widodo on Sunday came after a petrol bomb was thrown at the embassy of Myanmar in the capital, Jakarta.
The embassy attack early on Sunday, which police said caused a small fire, came against the backdrop of mounting anger in Indonesia - home to more than 202 million Muslims - over violence against the Rohingya in Myanmar.
A police officer patrolling a street behind the embassy spotted a fire on the second floor of the building and alerted police officers guarding the front gate, a Jakarta police statement said.
After the fire was extinguished, police found a shattered beer bottle with a wick attached to it, the statement said, adding the unknown perpetrator is suspected to have driven away from the scene. Jakarta police are investigating the incident, said spokesman Argo Yuwono.
Rohingya activists held a demonstration at the embassy on Saturday calling for the Nobel Prize Committee to withdraw the Nobel Peace Prize from Myanmar leader Aung San Suu Kyi, state news agency Antara reported.
Protests continued on Sunday in Jakarta's city centre with dozens of people calling for the Indonesian government to become actively involved in efforts to end human rights violations against Rohingya Muslims in Myanmar.
President Widodo said he sent Marsudi to Myanmar to hold "intensive communications" with involved parties, including the United Nations.
"Earlier this afternoon the foreign minister has departed to Myanmar to ask the Myanmar government to stop and prevent violence, to provide protection to all citizens - including Muslims in Myanmar - and to give access to humanitarian aid," Widodo said.
Widodo added that concrete actions are needed, and the Indonesian government is committed to helping to solve the humanitarian crisis.
Marsudi will also travel to Bangladesh, where tens of thousands of Rohingya have fled, to prepare additional aid for refugees there.
The treatment of Buddhist-majority Myanmar's roughly 1.1 million Rohingya is the biggest challenge facing leader Aung San Suu Kyi, who is accused by critics of not speaking out for the minority that has long complained of persecution.
Aid agencies estimate about 73,000 Rohingya have fled into neighbouring Bangladesh since violence in Myanmar erupted last week.
Source: News agencies