Australian Stosur is the reigning US Open champion and reached the final of Roland Garros in 2010 after making it to the semi-finals the year before.
Baltacha said: "It's not a great draw, let's be honest, but you can't always get those. I have massive respect for Sam because of what she's achieved and also how she goes about things but I do believe I have a chance against her.
"It will be a big match on a showcourt and I usually play well in those situations and I'll always fight for every ball. It's going to take one hell of a match from me but I've beaten top players before and I know what I'm capable of. I'm looking forward to it."
British number three Heather Watson, who reached the main draw for the second year running on Friday, will find out later who she will go up against.
Likewise number four Laura Robson, should she come through her final qualifying match against Karolina Pliskova of the Czech Republic on Friday.
World number one Victoria Azarenka has been drawn against Alberta Brianti, with a potential semi-final against Stosur.
Second seed Maria Sharapova faces Alexandra Cadantu with 13-times Grand Slam champion Serena Williams or Caroline Wozniacki likely to await in the quarter-finals.
Sharapova will complete a career Grand Slam if she wins on the clay.
Wimbledon champion Petra Kvitova plays wildcard Ashleigh Barty and is in line to face 2010 champion Francesca Schiavone or reigning champion Li Na in the last eight.
Venus Williams will make her first return to Slam action since revealing her autoimmune disease against Paula Ormaechea, with Agnieszka Radwanska next for her then 2009 French champion Svetlana Kuznetsova.