Martins sustained the injury against Kashima Antlers in the Asian Champions League on Tuesday.
The 33-year-old forward was carried off midway through the first half of the continental club fixture which they drew 2-2.
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.
He scored a hat-trick for Shanghai on Saturday in their 4-2 league win over Hebei China Fortune.
The injury ends any faint hopes Martins may have had of making Nigeria coach Gernot Rohr’s squad for this year’s World Cup in Russia.
Tuesday’s draw also means Shenhua cannot qualify for the knockout rounds of the continental championship.
Shanghai Shenhua are currently sixth in the CSL standings after four games.