Randall, who competed at last year's London Games but failed to make the final, acknowledged receipt of the Jamaica Anti-doping Commission's notification of her adverse finding for a banned diuretic but, like Powell and Simpson, denied knowingly taking a performance-enhancing substance.
"I have not intentionally taken any banned substance. I have been vigilant with everything I consume, so I am extremely shocked and surprised by this incident," Randall said.
The 25-year-old, who holds the Jamaican discus record with a distance of 61.21 metres, said she did not have the desire or the means to cheat.
Reuters sources said she had tested positive for the banned drug Hydrochlorothiazide, which reduces blood volume.
"I have never even seen steroids and don't know the first thing about them," Randall said.
"I am willing to undergo any other testing methods to prove my innocence. I love throwing the discus for my country and I hope this incident clears up after my 'B' sample has been tested."
Powell and Simpson confirmed that they tested positive for the stimulant Oxilofrine (methylsynephrine) while two more Jamaican athletes are reported to have failed tests at the same championships.
Agent Paul Doyle told Reuters that both athletes would request their 'B' samples are tested.
"We'll have to make the request this week, so from that point I'm not sure how long it takes, but I would imagine within the next 10 days to two weeks it will be tested," Doyle said.
Italian media reported on Monday that police had raided a hotel in the north of the country where sprinters had stayed and that several products had been seized.
Police said that the rooms of Canadian trainer Chris Xuereb had also been searched but that nobody had been arrested.
Stephen Francis, the coach of Powell and Simpson at the MVP track and field club, told Reuters from Lignano, Italy on Monday that Doyle had introduced Xuereb to Powell in May.
"This has nothing to do with us (MVP track club) and we are not disowning Asafa ... all we are saying is that this is his personal employee.
"He was not recommended by us, we don't know anything about him. He's not an MVP employee or MVP staff," Francis added.
American former double world champion Tyson Gay also said on Sunday that he had tested positive for a yet-to-be-revealed substance.
Gay, who has run the year's three fastest 100 metres times, had been expected to challenge Jamaican Olympic champion Usain Bolt at next month's world championships in Moscow.