By 2033, none of its debit or credit cards will have a strip, with banks in many regions including Europe able to issue the strip-less cards from 2024.
The UK moved to chip-and-pin for all card payments in 2006, but in the US, some magnetic strip systems are still in use.
Mastercard says chip-and-pin and new biometric cards that use fingerprints, offer greater security. The firm claims to be the first payment network to phase out the technology.
A spokesperson told the BBC the level of global acceptance of chip-and-pin was such that the time was right to begin phasing out the magnetic strip.
The slow phasing out is to leave what the firm calls a “long runway” for companies accepting payments to move to chip-and-pin.