Jamat-ul-Ahrar's spokesman Ehsanullah Ehsan and other members together Friday posted comments on Twitter about Malala and the award, stating that she did not represent Islam, Dawn online said.
Ehsanullah threatened that fighters would continue to strike people who took what to them was anti-Islamic positions.
Pakistani girl child education campaigner Malala Yousufzai and Indian child rights activist Kailash Satyarthi were awarded the 2014 Nobel Peace Prize by the Norwegian Nobel Committee for their struggle against the suppression of children and young people and for the right of all children to education.
Malala, 17, was shot in the head by Taliban militants in October 2012 in her home town in Swat district due to her defiance of the Taliban's ban on girls' education.
The Pakistani Army announced last month that a group of ten Taliban militants, who were allegedly involved in attacking Malala Yousufzai, had been arrested by the security forces.
The arrested militants admitted that TTP chief Mullah Fazlullah plotted the attack on Malala.