Sinn Féin President Mary Lou McDonald said she apologised for their “failures”.
It had emerged that three Sinn Féin offices received £10,000 payments from the fund, which have since been repaid.
MP and MLA constituency offices are ineligible for the scheme.
In a statement, Ms McDonald said she had accepted the resignations of Mrs McCallion, as a senator in the Seanad (Irish Senate), as well as the chair of the party’s Upper Bann constituency association and an official in the party’s west Tyrone office.
She said she had accepted the resignation of the west Tyrone official who had failed to return the money “despite being requested to do so” by MLA for the area, Maolíosa McHugh.
Mrs McCallion apologised “unreservedly” on Thursday afternoon, saying the grant was lodged into a joint account of which she is a named signature with her husband.
“I fully accept that as a named signature on the account that I should have taken extra steps to verify this situation, before it was brought to my attention on Tuesday.”
She said the money was repaid in full on Tuesday.
Payments from the fund were sent out automatically to 7,000 bank accounts, but it has emerged that some of the accounts which received the money were ineligible.
Sinn Féin said its offices did not qualify nor did it apply for the scheme.
The party said the funds received by three of its offices had been returned to Land and Property Services, which administered the grant.
But Ms McDonald said the money was only paid back on Monday and Tuesday of this week, months after they were received.
She said all those involved had been “censured” by the Sinn Féin Ard Chomhairle (party executive).
“Last night I accepted the resignation of Senator Elisha McCallion. She accepts full responsibility for the failure to return the grant immediately,” she said.
Sinn Féin vice-president Michelle O’Neill tweeted that the party viewed the situation very seriously and had taken “decisive action”.
Ms McDonald added that the chairperson of the Upper Bann constituency organisation had tendered their resignation after failing to return the money in a “timely fashion”.
“The Small Business Grant scheme was established to support struggling businesses in times of extraordinary hardship,” she said.
“The failure to immediately return grants erroneously paid into Sinn Féin accounts is a most serious situation.”
Figures released by the Department for the Economy (DfE) show that 24,700 payments were processed under the Small Businesses Grant Support Scheme.
There were 452 payments, totalling more than £4.5m, which were made to those who may not have been eligible.
The DUP, SDLP, Ulster Unionist Party and Alliance have all said that none of their MPs or MLAs received money from the Small Businesses Grant Support Scheme.
Earlier on Thursday, it emerged that the landlord of a DUP office received a payment from Stormont’s emergency Covid-19 fund for small businesses.DUP MLA Gary Middleton said he did not know which office was involved.
Mr Middleton told the BBC’s Good Morning Ulster on Thursday: “I can be very clear in terms of DUP MLAs, MPs, representatives, that no payments were made to those elected reps.
“I am led to believe that there was one case of a landlord having received the payment.
“That landlord should repay that money if that is the case.”
Mr Middleton said he was not aware if the money had been repaid.
He said the assembly standards commissioner should investigate the Sinn Féin payments, adding the party faced “serious questions” about when the funds were returned.