Although he doesn't count as a 'person,' Secretariat was the first 'athlete' to be featured on all three magazine covers in the same week. This was in 1973.
http://espn.go.com/classic/biography/s/Secretariat.html I found several sites that state, 'Only six times in history have Time, Newsweek and Sports Illustrated all had the same entity on their cover. They are O.J. Simpson, Mary Lou Rhetton, the 1980 U.S. Hockey Team, Joe Namath, Reggie Jackson and Secretariat.''
I looked for, and didn't find, confirmation on Namath, and since it doesn't mention Nadia Comaneci, I didn't bother looking for the rest.
Others I did find, however, are the US Womens World Cup Soccer Team (who were also on People magazine the same week) and Brandi Chastain.