According to the listing, this photo bares the stamp of the Bushnell company in San Francisco. On the back of the photo Houdini himself has written: "Taken 1899 July -- I was 24 years old." It appears Houdini had first written 1898, but then overwrote a "9", which actually makes him 25.
So this was taken during Houdini's first tour of the West Coast under the management of Martin Beck, which pre-dates his breakout fame by several months. It's interesting that publicity shots taken before this (the few that exist) all show Houdini in the guise of a very traditional magician. These were clearly taken to sell the new Harry Houdini -- King of Handcuffs! It worked.
By the way, this was listed on eBay with a starting price of $3,300, but the auction was ended early by the seller before any bids were made.
Mahatma ad from 'Houdini A Pictorial Life' by Milbourne Christopher. You can see five different Bushnell photos on pages 48-49 of 'Houdini His Legend and His Magic' by Doug Henning.