The verse read: "I will trust the Lord with all my heart and lean not on my own understanding; in all ways - acknowledge Him and He will direct my paths."
Detective Senior Sergeant John van den Heuvel said it was a "rather bizarre and brazen thing to do".
"We can't rule out the possibility that Mei's killer has returned to the scene.
"If it is the killer, it may indicate they're experiencing some sort of personal conflict over Mei's death and are now looking to religion for comfort."
The card was left in Ms Fan's bedroom next to a photo of her.
Mr van den Heuvel said that action created "a bit of a paradox, to brutally kill a young mother and then leave a religious verse of this nature".
The card had undergone forensic examination which strongly suggested its edges were cut commercially. The printing on the card was from an ink-jet printer which were common in homes.
Police believed someone broke in to the house between December 3 and 17 last year and were appealing to anyone who recognised the card or could provide information about why the verse might be significant to someone they know to contact them.
The new details in the case were aired on the show Police Ten-7 tonight.
Police were also continuing to appeal to the public for any sightings of anyone acting suspiciously in the Brussels Street area on the day of Ms Fan's death, or sightings of a 1992 bronze-coloured Toyota Corona with a black strip along the bottom of the doors and its front left hubcap missing.
Details had earlier been released of the murder weapon, which was found at the scene - a 32cm knife with a wooden handle with the word 'CARVER' stamped into the base.
The knife had been featured as part of a supermarket promotion in the early 90s so was relatively common, police said.
However, the knife used on Ms Fan had several distinctive features, including a missing third rivet in the handle, unusual scrapes from being sharpened and a bent tip of the blade.
It was possible the knife, which was originally part of a set, may have been disposed of as part of a deceased person's estate, sold in a garage sale or been donated to a second-hand or charity store, police said.
In recent weeks, police dive teams had also been searching the waters around Miramar Peninsula in a hunt for clues in the case.