Duque-Marino will be joined in the competition by Germany's Mona Barthel who was also a late replacement for compatriot Andrea Petkovic, who withdrew with an ankle injury on Wednesday.
Kanepi, ranked 16, reached the quarter-finals of the French Open in June, but has failed to recover from the foot injury that ruled out her out of Wimbledon.
"It's very sad that I cannot participate in the Olympics," Kanepi said on the International Tennis Federation website (www.itftennis.com).
"I do not know if I will ever get another chance to participate in the Olympic Games."
Kanepi's injury opened the door for 22-year-old Duque-Marino.
She gained an ITF place into the 64-strong women's singles competition which will take place at Wimbledon from July 28 to August 4.