After visiting the clinic, a police officer and judge decided to investigate further and took blood and urine samples which tested positive for cocaine.
Maximo Costa Rocha, the police chief for the Uruguayan province of Maldonado, told a news conference on Wednesday: "I have been authorised by a judge to inform you that our test (blood and urine) has resulted positive for cocaine."
Mr Costa Rocha said police first looked into the case when Maradona was admitted to hospital in the Uruguayan beach resort of Punta del Este on Tuesday, suffering from what his doctors said were hypertension and an irregular heartbeat.
After visiting the clinic, a police officer and judge decided to investigate further and took blood and urine samples which tested positive for cocaine.
The police chief said another sample had been taken and was being analysed to pinpoint when the cocaine was ingested.
Maradona, who has been in intensive care at the hospital, was expected to leave the unit to be transferred to a normal ward.
However the 39-year-old footballing star will later face police questions into the matter.
Mr Costa Rocha made it clear that neither Maradona nor anybody else had been arrested, but said several other people were helping police with their inquiries.
Assuming the test findings are confirmed, it is thought that the police will be concerned with discovering where Maradona obtained the drugs, rather than punishing the player for personal use.
"The trafficker is the delinquent, the consumer is the victim. That is why he is not detained and it is the trafficker we are looking for," Mr Costa Rocha said.
There has been much speculation that the football star's illness might be drug-related, given that he has undergone repeated treatment for drug addiction in recent years.
Maradona's career went into decline in 1991 when he was suspended for 15 months following a positive test for cocaine while playing for Napoli in Italy.
He was sent home from the 1994 World Cup in the US after failing a drug test for ephedrine, and was later banned for 15 months.
Maradona failed another drug test in 1997 after a match between Boca Juniors and Argentinos Juniors. However there were doubts about the validity of that sample.
20th century sportsman
The controversial soccer star won a World Cup winners medal in 1986 after Argentina beat Germany in the final.
Maradona, recently voted Argentine sportsman of the 20th century, also hit the headlines in the same competition when he apparently handled the ball when scoring against England in the quarter final.
When asked about the incident he described it as "the hand of God".
Maradona also led Argentina to the 1990 final, where the Germans avenged their 1986 defeat.