Rizwan and Irfan both suffered hamstring injuries in the third match in Rawalpindi, where a second-string New Zealand side won by seven wickets to level the five-match series 1-1
Sangakkara became the first non-British president of the MCC, the custodian of cricket's laws, when he took over in October last year.
The disruption caused by the outbreak prompted the MCC committee to offer the 42-year-old to continue until Sept 30, 2021, a motion likely to be approved in its June 24 annual general meeting.
"Whilst Presidents of MCC only normally serve for a twelve-month period, it is not unprecedented for longer terms to be introduced to respond to extraordinary circumstances," MCC said in a statement, citing the stints of Lord Hawke (1914-18) and Stanley Christopherson (1939-45).