Petkovic, a 2011 quarter-finalist in Melbourne, won the first set 7-6 in the blistering heat.
However, as she trailed 4-3 in the second, the German world No 64 collapsed to the ground.
Medical officials raced onto Court 5 and checked the 31-year-old’s pulse and blood pressure.
Petkovic attempted to quickly rise to her feet but was initially unable to do so.
She consequently retired from the match and appeared wobbly when embracing opponent Begu for a brief hug.
Heat stroke is thought to be the cause of the incident, although it has yet to be officially confirmed.
Temperatures were expected to soar to about 36-37 Celsius (96-99 Fahrenheit) on day one, although they fell shortly before the prediction.
Meanwhile, the women’s side of the draw is wide open this year with no clear favourite.
Serena Williams is odds on with the bookmakers to scoop the season-opening Grand Slam.
But John McEnroe is unsure who will come out on top over the next fortnight.
“I think the reason [Williams] still plays is because she is the favourite and she can still win the big titles, she wants to win the big Grand Slams and break the records,” McEnroe told Eurosport.
“She hasn’t played since the US Open, but she played Hopman Cup, she looked good, looked in good form.
“She is one of the top favourites, though there isn’t the top favourites on the women’s side like there is on the men’s.
“But I think she is one of perhaps, three players, that I think will win the title.”