The grainy video, sent to the 20 Minuten newspaper, is the first sign of life of the couple since the dramatic prison-break on February 9th.
In it 32-year-old Angela Magdici is seen apologizing to her family for her actions and describing Hassan Kiko, 27 as “the love of my life”.
Kiko, sentenced for the rape of a 15-year-old and doing time in the Limmattal prison, also appears in the film, maintaining his innocence.
Zurich cantonal police said the video would form part of their investigation.
In the video a butterfly patterned cloth covers the table at which Magdici sits, and a crucifix is seen on the wall behind her partner.
A former Basel detective inspector told the paper investigators would be trying to establish who had provided the video and where it was shot.
Markus Melzl said the distinctive cloth could yield clues as to the couple's whereabouts.
It was so unusual that anyone who had seen it would likely remember, he said.
However, newspaper readers reported that the same tablecloth was available to purchase on Ebay and that the German-based trader sold throughout Europe.
The former detective said something must have changed in the couple's circumstances for them to have taken the step of releasing the video message.
“There must be a reason why they have broken their silence after such a long time,” Melzl said.
Meanwhile the Blick newspaper online quoted a private detective as saying the release of the video was a "big mistake" that greatly increased the chances of the couple being caught.
The married prison guard and the inmate escaped from the Limmattal prison in a black BMW X1 station wagon.
Police believed they were headed for Italy. But Magdici's husband said at the time he believed they were bound for Syria.