According to a recent report, Microsoft plans to keep Call of Duty on PlayStation for "several more years" past the marketing deal the latter currently has with Activision.
This comes from The Verge, which recently received a statement from head of Xbox Phil Spencer. "In January, we provided a signed agreement to Sony to guarantee Call of Duty on PlayStation, with feature and content parity, for at least several more years beyond the current Sony contract, an offer that goes well beyond typical gaming industry agreements," wrote Spencer in the statement.
It had already been noted that the next three Call of Duty games would launch on PlayStation, which obviously includes the upcoming Call of Duty: Modern Warfare 2. Presuming that Activision keeps up the yearly releases of the series, that means there will be Call of Duty games on PlayStation until at least 2024, and now, further beyond that.