The caning comes less than two weeks after a male couple were flogged nearly 80 times each for having gay sex, which is outlawed under local Islamic law.
On Monday, the two accused received 40 lashes each from a masked sharia officer who beat their backs with a stick.
One of them, identified only as JF, said he chose flogging to avoid a criminal prosecution that could have seen him jailed up to six months.
"The Sharia police gave us options and we consciously decided to comply with the Islamic criminal code. No one forced me to choose it," he told AFP.
Aceh is the only province in the world's most populous Muslim-majority country that imposes Islamic law.
Non-Muslims who have committed an offence that violates both national and religious laws can choose to be prosecuted under either system.
Flogging of non-Muslims is rare, however, with only a handful subjected to the punishment in recent years for crimes including gambling and selling alcohol.
The two Christians were among seven people publicly flogged in the province on Monday.
The five others were Muslims who were whipped for adultery and drinking alcohol - both violations of religious law.
Human rights groups have slammed public caning as cruel, and Indonesia's President Joko Widodo has called for it to end.
Follow us on Facebook, Twitter and Instagram to stay connected