Yates, one of the brightest prospects in British cycling, failed the test due to an "administrative error" over the use of an asthma inhaler, his team Orica-GreenEDGE said.
The UCI said in a statement that Yates had not been suspended because "such a substance does not entail imposition of a provisional suspension".
The Bury-born 23-year-old had returned an adverse analytical finding for Terbutaline, a common treatment for asthma, from a test conducted at the Paris-Nice stage race last month, Orica-GreenEDGE said in a statement.
"The substance was given in an ongoing treatment of Simon Yates' documented asthma problems," the Australian team said.
"However, in this case the team doctor made an administrative error by failing to apply for the TUE (therapeutic use exemption) required for the use of this treatment.
"This is solely based on a human error that the doctor in question has taken full responsibility for," they added.
"There has been no wrongdoing on Simon Yates' part. The team takes full responsibility for this mistake and wishes to underline their support for Simon during this process."
In its statement, the UCI said: "As per the UCI's anti-doping rules, such substance does not entail the imposition of a provisional suspension.
"The rider has the right to request and attend the analysis of the B sample. At this stage of the procedure, the UCI won't comment any further."
Orica GreenEDGE added it was submitting documentation to the UCI in order to clarify everything.
Yates, the twin brother of fellow professional cyclist Adam, won the points race title at the 2013 world championships in Minsk.
The positive test is another blow to British Cycling which has been rocked by the departure of technical director Shane Sutton this week following allegations of sexism and discrimination.
Yates received backing from one of his British team mates Owain Doull.
"Tweet my thoughts on Yatesy yesterday and people calling me naive and stupid for believing in him," he said on Twitter.
"I'm not naive, I just know and trust the lad I raced and lived with for years and have seen first hand how he has struggled with asthma."
(Reporting by Ian Ransom in Melbourne and Ian Chadband in London; Editing by Peter Rutherford and Ed Osmond)
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