Former Olympic champion Joshua beat Wladimir Klitschko in the 11th round of a brutal bout in London on April 29, and the 50-year-old Tyson was deeply impressed.
Joshua, 27, put the 41-year-old Ukrainian on the canvas in round five but was floored himself in the following round before digging deep and stopping Klitschko with a technical knockout.
"The test that he overcame in his last fight with Klitschko, the sky is the limit for him," Tyson told CNN Sport.
"When you have a great heavyweight fighter ...you got to punch like that and make people happy and hurt people. [For] all those other little guys it's over, especially for a heavyweight he appears to be, he's going to suck all the air out of the room.
Tyson was particularly impressed by the way Joshua recovered after Klitschko had put him down.
"He could have stayed down from that punch. Most new guys that get hit with a punch like that they normally stay down, also they lose their confidence once they get up.
"He stayed composed -- he was a little dizzy at first -- but for a young fighter with 18, 19 fights he did awesome."
Joshua, who won Olympic heavyweight gold at London 2012, took his unbeaten professional record to 19 wins with 19 knockouts.
Tyson, nicknamed "Iron Mike," won his first world title at the age of 20 in 1986 and went on to dominate the division in a savage and often controversial career until his 1996 defeat by Evander Holyfield signaled the end of the New Yorker's boxing domination.