The officer has been identified as Lieutenant Colonel Faisal Malik, while the soldier's identity is yet to be revealed.
The clashes also left six militants dead.
The news came after armed forced initiated a ground operation in the Shawal area of North Waziristan on August 20.
Read: Army launches ground operation in Shawal, NWA
According to Director General Inter Services Public Relations (ISPR) Asim Bajwa, the ground operation was being carried out on the direction of the army chief, adding that air and ground offensives should be coordinated.
Army chief General Raheel Sharif directed all military objectives to be achieved as soon as possible.
Funeral prayers held
Funeral prayers of Lt Col Faisal Malik and Sepoy Zohaib Shaheed, who were killed in Shawal on Monday, were held at Army Graveyard, Race Course Ground in Rawalpindi.
A large number of senior serving and retired officers, including Chief of General Staff Lieutenant General Zubair Mahmood Hayat, Corps Commander Rawalpindi Lt Gen Qamar Javed Bajwa, DG Joint Staff Lieutenant General Najibullah Khan, other senior officers and relatives of the deceased offered the prayers.
The slain soldiers will be buried in their ancestral villages with full military honours.
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