The conflict erupted on the first working day of the holy Islamic month of Ramadan, when food imports from Pakistan usually peak in Afghanistan, which is facing a humanitarian and hunger crisis.
A 10-day-old closure of the Torkham border point has stranded thousands of trucks filled with essential goods.
The Taliban-run Afghan Interior Ministry said on Monday the latest firing took place overnight and that one Taliban fighter had been killed and two injured.
Two Pakistani security officials, speaking on condition of anonymity, said that members of the Pakistani security forces had been wounded.
Pakistan's foreign office did not respond to a request for comment.
The neighbouring countries have a strained relationship, with Pakistan saying that several Islamist militant attacks that have occurred there have been launched from Afghan soil - a charge the Taliban deny.
Pakistani military aircraft carried out strikes that killed dozens on Afghan territory in December.
Abdul Mateen Qaniee, the Afghan interior ministry spokesman, said that this week's clashes had been resolved but did not comment on whether the border crossing would reopen.
It has been shut since February 21.
The latest closure, which chamber of commerce officials said was sparked by a dispute over the construction of a border-area outpost, has left 5000 trucks stranded and traders alarmed at rising losses.
"This is a very serious issue and is badly affecting trade between the two countries," said Ziaul Haq Sarhadi, director of the Pakistan-Afghanistan Joint Chamber of Commerce.
The Torkham crossing is the main transit artery for travellers and goods between Pakistan and landlocked Afghanistan.
Trade between the two countries was worth more than $US1.6 billion ($A2.6 billion) in 2024, according to Pakistan's foreign office.
Yousaf Afridi, president of the Chamber of Commerce and Industries for Pakistan's Khyber district where the Torkham crossing is located, said the closure had caused at least $US15 million in losses.
It could exacerbate the challenges confronting the Afghan economy, which has teetered near crisis since the Taliban took over in 2021, leading to a cut in development aid and sanctions affecting the banking sector that has hampered businesses.
Millions of Afghans are at risk of hunger and around half the population needs humanitarian assistance to survive, according to the United Nations.
