Støjberg received 28,420 personal votes in Denmark's June election, more than any other party figure apart from party leader Lars Løkke Rasmussen, reflecting the support of many Danes for her tough rhetoric and policies on immigration.
But she was blocked from taking one of the party's top posts at a meeting of its 43 members of parliament on Monday.
Former foreign minister Kristian Jensen, a relative moderate, was voted back in as the party's deputy chair with Jakob Ellemann-Jensen voted back in as political chair.
Søren Gade, a party grandee and former defence minister, told TV Midtvest that he was disappointed by the decision.
“Inger's position has a strong support among the public. There are many people who are worried about immigration,” he said.
“I'm worried about who will now represent that point of view, which has been the reason why so many people returned to the Liberals in the most recent election.”
Even Kristian Thulesen Dahl, leader of the Danish People's Party, which has good relations with Støjberg, said he was disappointed.
“What just happened? The Liberals have blocked Inger Støjberg from the leadership,” he wrote on Twitter. “Of course, it's entirely up to them to decide on their own constitution, but if it reflects a political shift in immigration policy, it obviously raises concerns.”
Hvad skete lige der? Venstre vrager Inger Støjberg til ledelsen. De bestemmer selvfølgelig helt selv deres konstituering, men hvis det er udtryk for et politisk kursskifte i udlændingepolitikken, vækker det selvsagt bekymring! #dkpol #dkmedier
— Kristian Thulesen Dahl (@Kristianthdahl) August 5, 2019
Støjberg drove an extremely hardline immigration policy, bringing in a law allowing Danish police to strip refugees of cash and jewellery to help offset the cost of housing them (although the law in the end turned out to be purely symbolic).
She claimed to have passed more than 100 measures to tighten immigration, notoriously celebrating with a cake when she passed the 50th through parliament.
- Immigration minister panned by opposition over ill refugee deportation scandal
- Three years after Denmark’s infamous 'jewellery law' hit world headlines, not a single piece has been confiscated
- Danish Integration Minister Støjberg: I won’t repeat cake photo
With the party's leaders now returning from their summer break and starting to regroup following June's election defeat, a power battle has broken out, with some in the party wanting Rasmussen to step down.
Rasmussen made a cryptic comment on the question of whether he wants to hang on to the party's leadership in a video released on Facebook on August 2.
“I, and the Liberal Party, have the ambition of once again takng back the keys to the Prime Minister's office,” he said.
The political commentator Jarl Cordua told the Altinget political website that Støjberg's sidelining showed the parliamentary party overruling Rasmussen, who, according to his sources, had put her forward as vice chair, hoping to unite the party's left and right wing.
“Lokke tried a division of power, but unfortunately for him and for the party, it cracked,” Cordua said.
Instead, the parliamentary party voted the former Minister for Public Innovation, Sophie Løhde, to the post.
“There has been no clarification on who will be Lars Løkke Rasmussen's successor,” he said of the vote. “Inger Støjberg has been put back in the game. She is left without a seat in the group leadership, and she can't be happy with that at all.”