The keenly-watched meet in Naypyidaw comes as Suu Kyi, a Nobel Peace Prize winner, has been frozen out by a global rights community that once adored her, outraged at her tepid reaction to plight of the Rohingya.
After the talks in the capital Naypyidaw, the pontiff will address Suu Kyi and diplomats there -- his first opportunity to speak publicly about the conflict that looms over his trip.
Pope Francis, 80, late on Monday received a "courtesy visit" from the powerful army chief Min Aung Hlaing -- whose troops the UN and US believe have prosecuted a campaign of ethnic cleansing against the Rohingya from Rakhine state.
General Min Aung Hlaing has firmly denied allegations of widespread brutality by his forces, despite the flight of 620,000 Rohingya to Bangladesh since August.
His office said he told the pope there was "no discrimination" in Myanmar, vaunting his military for keeping "the peace and stability of the country".
The pope has repeatedly spoken out from afar about the crisis, standing up for his Rohingya "brothers and sisters".
A similar embrace in Myanmar is fraught with danger -- using the term "Rohingya" is unacceptable in a country where the Muslim minority are denied citizenship and branded illegal "Bengali" immigrants.
The country is listening closely to see if Francis will name the Rohingya on Myanmar soil, and risk provoking the outrage of Buddhist nationalists.
Early Tuesday, day two of four-day visit, the pontiff attended an inter-religious meeting in Yangon, where he met leaders from Buddhist, Muslim, Baptist and Jewish faiths.
He flies up to the capital Naypyidaw Tuesday afternoon to meet Aung San Suu Kyi.
So far, the pontiff has received a warm welcome to the majority Buddhist nation.
Myanmar's Catholic community numbers just over one percent of the country's 51 million people.
But some 200,000 Catholics are pouring into the commercial capital Yangon from all corners of the country ahead of a huge, open-air mass on Wednesday.
Zaw Sai, 52, from Kachin state found space for him and his family to camp out in a church ground.
"We feel very pleased because we are from different ethnicities but are one in our religion," he told AFP.
Just days before the papal visit, Myanmar and Bangladesh signed a deal to start repatriating Rohingya refugees within two months.
But details of the agreement -- including the use of temporary shelters for returnees, many of whose homes have been burned to the ground -- raise questions for Rohingya fearful of returning without guarantees of basic rights.
Pope Francis will travel on to Bangladesh on Thursday.