Takeda Pharmaceutical Co. shares tumbled the most in almost a decade after Moody’s Investors Service cut the drugmaker’s credit rating and investors reacted to adjustments in equities indexes related to its $62 billion acquisition of Shire Plc.

Investors may be shifting their positions on the two drugmakers after index providers in London and Tokyo announced details of how their gauges will reflect the impact of Shire merging into Takeda. The FTSE Russell and MSCI said they would remove Shire...