A second sample from Miller's test is said to have shown positive for the weight loss and energy stimulant GW1516.
The US broadcaster ESPN has reported that the second sample also showed the human growth hormone HGH.
Promoter Eddie Hearn is now scrambling to find an opponent for WBA, IBF, WBO and IBO champion Joshua's US debut at Madison Square Garden in New York on June 1.
Undefeated Miller, 30, said : "I messed up. There were a lot of ways to handle the situation, I handled it wrongly and I'm paying a price for it.
"I messed up a big opportunity and I'm hurting on the inside. My heart is bleeding right now - I hurt my family, my friends, my team, my supporters.
"But, I'm owning up to it. I'm going to deal with it. I'm going to correct it. I'm going to come back better and I'm humbled by the experience."
Miller was instantly denied a license to box by the New York State Athletic Commission after the announcement of the first failed test.
Then Hearn said he had been informed of Miller's second adverse finding by the Voluntary Anti-Doping Association.