Ko Ni, a legal advisor to the National League for Democracy who spoke out against rising sectarianism, was shot in the head yesterday by an assailant as he waited outside the airport while holding his grandson.
A taxi driver who tried to stop the attacker was also gunned down in an act that has shocked a country unused to political killings.
The unnamed attacker was arrested at the scene and is being interrogated by police but authorities have so far remained silent on his motivations.
"We strongly denounce the assassination of Ko Ni like this as it is a terrorist act against the NLD's policies," the statement said.
More From This Section
The 63-year-old was a veteran member of the party which doggedly faced down decades of military rule to sweep the 2015 elections that brought Suu Kyi to power.
As a prominent Muslim party member he was also a rare voice advocating religious tolerance and pluralism -- and a critic of the powerful military's ongoing political influence.
"As we are from a different religion there were many people who didn't like and hated it. I think that also could be a reason (for his murder)," she told DVB TV outside the hospital where her father's body had been taken.
Myanmar's border regions have simmered for decades with ethnic minority insurgencies.
But it is rare for prominent political figures to be murdered in Yangon, the country's booming and largely safe commercial hub.
Around five per cent of Myanmar's population is Muslim.
Suu Kyi has herself faced criticism for not fielding a single Muslim candidate during the 2015 elections, a move analysts said was a sop to Buddhist hardliners.