The note on the back says: "This is a picture of the girl I love. Since we both love this country I leave it here and when everything works fine with us both might pick it up and I'll ask her to marry me. Please leave the picture here! Thanks."
Arts Centre chief executive Philip Aldridge said staff would love to reunite the author of the note, who seemed to be from overseas, with the photograph.
"If we're able to return the photo to them, we'll tell them we're sorry we had to remove it, but I'm sure they'll understand why," he said.
"We really hope the author and their girlfriend had a happy ending too, even though the photo hasn't yet been collected."
Access to the observatory was restricted after the city's September 2010 earthquake, and ended with the tower's destruction by the earthquake in February 2011.
Its reconstruction is costing the Arts Centre trust $10 million.
The find is among the more unusual at the Arts Centre, where workers have unearthed a great variety of items since the $290 million, 10-year restoration programme began in 2012.
Notable finds include a large rat skeleton, a terse letter from a man to his ex-wife from the 1970s, a hooded seal jaw, and a boxing glove.
The centre is being progressively reopened to the public. So far 11 of the 23 buildings are open, with the observatory a key part of the second restoration stage.