Kakubo, who had been foreign minister since September 2021, said in a letter he was quitting because of "malicious claims over a business transaction."
Earlier, a video showing two people counting wads of cash stacked on a table spread quickly on Zambian social media accounts.
An image of a signed handwritten note, dated July 8, 2022, was also put online. The note named a Chinese mining firm and a Zambian mining firm and said they had "exchanged $100,000."
Though the names of Kakubo and a Mr. Zang were on the note, it was not immediately possible to verify the details.
President Hakainde Hichilema has accepted Kakubo’s resignation, an official statement said.
It gave no reason for the resignation but added: "The president acknowledges the commendable work and leadership" of Kakubo in the government.
Kakubo, 43, quickly followed the announcement by releasing his own letter.
He said he had resigned "in view of the matter that is currently in the media regarding malicious claims over a business transaction between my private family business and our business partner with whom we still have good relations."
"This decision is to ensure that our government is not distracted from continuing to look for solutions for bettering the lives of our people," he said.
Kakubo could not be reached for further comment on his resignation or the video.
Chinese enterprises are heavily involved in the Zambian mining industry, a bedrock of the southern African nation's economy. China is a major importer of Zambian copper.
Kakubo, a member of parliament since 2016, said he would remain loyal to the government. And the president's statement said Hichilema "implores" the former minister "to continue to serve diligently in his capacity as member of parliament."
The Chinese embassy said in 2022 that more than 600 Chinese businesses had invested more than $3 billion in Zambia.
China has also been a major player in international efforts to restructure Zambia's foreign debt. Zambia defaulted on its sovereign debt in 2020 as the COVID-19 crisis grew.
