There was no independent corroboration of the report on Sunday, which appeared in the newspaper al-Hayat under an Islamabad dateline and cited sources close to the Islamist network.
The newspaper claimed al-Qaida bought the weapons in suitcases in a deal arranged when Ukrainian scientists visited the Afghan city of Kandahar in 1998.
The city was then a stronghold of a Taliban government that refused to hand over Usama bin Ladin for trial abroad.
The report claims al-Qaida could use the weapons inside the United States or anywhere else should the network face a "crushing blow" which threatened its existence.
Ukraine inherited nuclear weapons from the Soviet Union but in 1994 it agreed to send 1900 nuclear warheads to Russia and sign up to the Nuclear Non-Proliferation Treaty.
After the Soviet Union broke up in 1991, a former Russian National Security Adviser, Alexander Lebed, said that up to 100 portable suitcase-sized bombs were unaccounted for.
Moscow has denied such weapons existed, but Lebed said each one was equivalent to 1000 tons of TNT and could kill as many as 100,000 people.
Al-Hayat did not say how many weapons al-Qaida bought or say who exactly had provided them.
The United States has repeatedly said its worst fear is that a group like al-Qaida might obtain access to weapons of mass destruction and use them against the American people.