Martins sustained the injury in Shanghai's 2-2 draw against Kashima Antlers in the Asian Champions League on Tuesday when the 33-year-old was carried off midway through the first half.
The former Inter Milan and Newcastle United forward joined Shenhua at the start of the 2016 CSL season from Major League Soccer side Seattle Sounders and scored a hat-trick for Shanghai on Saturday in their 4-2 league win over Hebei China Fortune.
Tuesday's draw means Shenhua cannot qualify for the knockout rounds of the continental championship, while Wu Jingui's side are currently sixth in the CSL standings after four games.
(Reporting by Michael Church; Editing by Christian Radnedge)
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