He said the Taliban fighting Karzai's government profited from drugs, but Karzai was reluctant to move against big drug lords in his political power base in the south, where most of the country's opium and heroin is produced.
"Karzai was playing us like a fiddle," Schweich wrote.
"The US would spend billions of dollars on infrastructure development; the US and its allies would fight the Taliban; Karzai's friends could get richer off the drug trade," he wrote.
"Karzai had Taliban enemies who profited from drugs but he had even more supporters who did."
Schweich also accused the Pentagon and some US generals of obstructing attempts to get military forces to assist and protect opium crop eradication drives.
Nato and US military commanders have been reluctant to get involved in the drug fight, arguing that destroying farmers' crops would alienate tribesmen and increase support for the Taliban.
Hillary Mann Leverett, a former US National Security Council official for Afghanistan, told Al Jazeera that the US knew that government ministers in Afghanistan, including the minister of defence in 2002, were involved in drug trafficking.
"Karzai was playing us like a fiddle. The US would spend billions of dollars on infrastructure development; the US and its allies would fight the Taliban; Karzai's friends could get richer off the drug trade"
ex-US state department co-ordinator for counter-narcotics and justice reform for Afghanistan
Afghan ministers at that time had little expertise but were appointed because "they were warlords, they were thugs, they represented various ethnic and sectarian constituencies", Mann Leverett said.
She added that the US government chose to work with them in an attempt to stop Afghanistan becoming a haven for al-Qaeda.
"Instead of funding the warlords we could have funded the UN to have a security peacekeeping force throughout the country.
"Instead we left Karzai without any troops, without any weapons, without any money, without any backing, to the warlords.
Gonzalo Gallegos, a state department spokesman, did not directly address Schweich's allegations but defended US policy and backing for Karzai.
"We know and understand that there is a corruption issue in Afghanistan but we're working with the sovereign government," Gallegos said on Thursday.
"President Karzai has shown us through word and deed that he is working with us to help improve the plight of that country."
Gallegos added that corruption was a deeply rooted problem and solving it would take time.
Drug production has skyrocketed since the US-led invasion that ousted the Taliban.
In 2007, nearly 200,000 hectares of land in Afghanistan was used to cultivate poppy - more than double the area in 2003 – and the country produced 93 per cent of the world's supply of opium, the raw material of heroin.
Karzai says his government is succeeding in the war on drugs and has repeatedly promised his US backers that he is committed to rooting out endemic corruption and fighting the drug trade.
His counter-narcotics ministry says 20 of Afghanistan's 34 provinces will be poppy-free this year, compared to 13 provinces in 2007.
But in the south, cultivation remains rampant.