The image was captured the day after the luxury liner sank in the Atlantic, killing more than 1,500 people.
It comes with a previously unpublished statement from the photographer, who describes seeing scrapings of red paint on the side.
The estimated guide price is between Â£10,000 and Â£15,000.
The photograph was taken by the chief steward of steamer the Prinz Adalbert, who was at the time unaware of the tragedy that had occurred the previous day.
RMS Titanic had been four days into a week-long trans-Atlantic crossing from Southampton to New York when the supposedly "unsinkable" ship struck the iceberg on 14 April 1912.
A lookout in the crow's nest, who had not been given binoculars, spotted the hazard just 37 seconds before the impact at 23:40 on 14 April.
The ship sank less than three hours later at around 02:20 on 15 April.
A statement by the chief steward of the Prinz Adalbert reads:  "The Titanic disaster was not yet known by us.
"On one side red paint was plainly visible, which has the appearance of having been made by the scraping of a vessel on the iceberg."
The document is then signed by the chief steward and three other crewmen.
Auctioneer Andrew Aldridge said: "The photograph was acquired not long after the Titanic's sinking by Burlingham, Montgomery & Beecher, attorneys for Titanic's owners, White Star Line.
"This photograph, regarded by generations of Burlingham maritime lawyers as "The Titanic Iceberg" hung on the firm's walls from 1913 until it closed its doors in 2002."
The lot will be auctioned by Henry Aldridge & Son in Devizes, Wiltshire on 24 October.
A photograph purporting to show the iceberg that sank the ill-fated Titanic is expected to fetch over Â£10,000 when it is sold at auction.