The 16-year-old, coached by Colin Baross at the Sports Training Village, produced her best clearance of 5.10m with her opening jump of the competition in the Olympic Stadium.
That ensured she was one of the top eight jumpers in the 12-strong field to progress to the final three of six jumps. New Zealand’s Anna Grimaldi won gold with a leap of 5.62m.
Maton is back in action on Saturday in the T47 100m heats, hoping to reach the final scheduled for 11.42pm BST on Sunday.
She touched the wall third in 4:49.49 behind Australia’s Lakeisha Patterson, who won in a world record time of 4:40.33.
The bronze represents Millward’s sixth Paralympic medal after four silvers and a bronze at London 2012.
Millward has been reclassified from S9 to S8 this year and said: “It’s been exciting because I’ve got a whole new set of competitors. I’ve got a few more races to come and I’m really excited for them.”