The 87-year-old had passed away a day ago.
He was the father of Supreme Court Justice Yahya Afridi and had also served as the Khyber Pakhtunkhwa chief secretary.
The people attended the funeral in large numbers, including Chief Justice of Pakistan Gulzar Ahmad Khan, Supreme Court and high court judges, politicians, current and former bureaucrats, lawyers and people from other walks of life.
Mr Omar, who had served as the minister for interior, state and frontier region and narcotics control in the interim government of PM Malik Meraj Khalid, belonged to the Adamkhel branch of Afridis.
He was born in London, UK, in Jan 1934. He had obtained education in Presentation Convent Murree, Bishop Cotton School Shimla (India), Karachi Grammar School, and Victoria College, Alexandria (Egypt).