The female victim, 38, was stabbed on Saturday in front of a supermarket in southern Bavaria by the 29-year-old migrant, police said, in a case that made national headlines.
The stabbing took place in front of the woman's children. The woman subsequently died from her wounds.
Police said motives of the assault have not been determined, and the man has since been interned in a psychiatric hospital.
But they confirmed that they are looking into a possible religious link after learning that the victim, a mother of two who arrived in Germany in 2011, was a Christian convert.
"It's a possibility that we're exploring," said a police spokesman, adding that the victim and the alleged attacker knew each other even if they were not close.
The man had arrived in Germany in 2013 and was residing at an asylum-seeker shelter.
Germany took in more than a million refugees since 2015, and some have taken on the Christian faith.