The 32-year-old, who played under HSV head coach Markus Gisdol at Hoffenheim between 2013-2015, was a free agent after his contract at Swiss side St. Gallen expired in the summer.
"Sejad is an experienced Bundesliga player, who has proved he has still got what it takes during his time away," said Hamburg sporting director Jens Todt. "Sejad is versatile and can help us in the short-term."
Salihovic made his professional breakthrough at Hertha, before moving to Hoffenheim in 2006. He famously saved the club from automatic relegation with two late penalties against Borussia Dortmund on the final day of the 2012/13 campaign, and left in 2015 as Die Kraichgauer's record appearance maker (249 outings in all competitions).
The former Bosnia-Herzegovina international returned to Europe with St. Gallen earlier this year, following a two-season stint at Chinese outfit Beijing Renhe.
He has registered 46 goals and 36 assists in 176 Bundesliga appearances to date.
Watch: Salihovic's heroics in the last day of 2012/13