"We will announce dates for her trips later," said Aye Min Han, information officer from the Mon State NLD.
She planned to make public speeches on March 27 and 29 marking General Aung San's 100th birthday.
Last week, there was a report that she sought a medical check-up at a Nay Pyi Taw hospital and missed parliamentary meetings during March 16-17.
Her family doctor Tin Myo Win has insisted that she is in good health.
"Aunty is in good health. Her trips were postponed as she's very tired due to her recent trips. And she is also due to attend Parliament. The rescheduling is not due to her health,” the doctor said.
Suu Kyi travelled to Mawlamyine, the capital city of Mon State in 2012, and to Kayin in January 2014.