A spokesman for Bandaranayake confirmed that she received the letter sacking her on Sunday, but declined comment.
No replacement has been named by the government.
Sri Lanka's Sunday Times newspaper said Rajapakse had offered to allow Bandaranayake to retire and so avoid impeachment during a meeting Saturday with other supreme court judges, but a source close to her told AFP that she was not amenable.
Rajapakse's spokesman would not comment on what was discussed in Saturday's meeting.
The ruling party initially framed 14 charges of financial, professional and personal misconduct against Bandaranayake, but later cleared her of financial wrongdoing and convicted her only on three counts of misconduct.
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Legislators had found her guilty of tampering with a case involving a company from which her sister had bought an apartment, of failing to declare dormant bank accounts, and of staying in office while her husband faced a bribery charge.
Bandaranayake walked out of a parliame