The 22-year-old life-long Dortmund fan broke into the Germany squad this season on the back of impressive form which has helped steer Dortmund towards their first German league title since 2002.
With his side currently seven points clear at the top of the table with six games left to go, Borussia are edging ever closer to the Bundesliga shield and a Champions League place next season.
But Grosskreutz, who scored as Dortmund came from behind to beat title rivals Hanover 4-1 at home last Saturday, is refusing to get a haircut until his team are crowned German champions.
"We are slowly getting towards the title and then I can get my haircut," he admitted.
"I have never had it so long before, I bet last October that I wouldn't get it cut until we win the league."
Hamburg coach Michael Oenning has said he hopes Dortmund win the title, but plans on pulling off an upset when they host the German leaders.
"I like Dortmund and would be happy if they are champion," said the 45-year-old, who took over after Armin Veh was sacked last month.
"But we will cook something up for them."
And Hamburg captain Heiko Westermann, who used to play for Dortmund's rivals Schalke, said he wanted to beat the leaders to open up the title race.
"We want to reward our hard work by beating Dortmund to make the league exciting again," said the Germany defender.
Hamburg are seventh in the table and four points off a place in the Champions League.
"We need the points not only for our confidence, but also to achieve our goals," said Oenning.