Randall, who competed at last year's London Games but failed to make the final, acknowledged receipt of the Jamaica Anti-doping Commission's (JADCO) 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 in a statement to Jamaican Radio station RJR 94 FM.
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.
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.
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.