The 21-year-old Romanian qualifier, ranked 66th in the world, won 10 of the final 13 games with her left thigh heavily strapped.
Niculescu called for trainer while leading 2-1 in the second set. The delay appeared to affect Chakvetadze's timing - she was broken in her next two service games and trailed 5-1.
In the third set, Chakvetadze double-faulted to hand Niculescu a 3-2 lead, and then netted a backhand to lose serve again and trail 5-2.
Chakvetadze is the second seeded player to lose at the indoor hard court tournament after No. 8 Daniela Hantuchova of Slovakia fell to Maria Kirilenko of Russia on Monday.
Also, Francesca Schiavone of Italy beat Caroline Wozniacki of Denmark 7-6 (3), 6-2, and 2007 Wimbledon finalist Marion Bartoli of France defeated Hungarian teenager Agnes Szavay 6-4, 6-0.
Patty Schnyder of Switzerland was to play qualifier Petra Kvitova of the Czech Republic later Tuesday, and fifth-seeded Agnieska Radwanska of Poland was to face Russian qualifier Vera Dushevina.
Top-seeded Hantuchova reaches quarterfinals
Casillas: We Must Protect Robinho
