Alphonsi, who won 74 caps for England, said she felt let down by Smith’s punishment.
The RFU does not have the power to remove council members, who are volunteers elected by their clubs rather than RFU employees.
A Warwickshire RFU statement read: “We would like to announce that Matt Smith has resigned from his position as chair of Warwickshire RFU, in light of a recent disciplinary process.
“We want to be clear that we take issues of sexism and misogyny seriously.”
On Monday the Women’s Leadership Collective wrote to the RFU calling for a change in its policy and to dismiss Smith.
The open letter said the punishment, following a three-person disciplinary panel, showed “a significant disconnect between the RFU’s stated commitment to zero tolerance of discrimination and the perception of how those principles are applied in practice”.
The RFU stipulates a “zero-tolerance approach” to discrimination and harassment and forbids public comment that could damage the game or the union’s reputation.
The letter from the Women’s Leadership Collective read: “We had hoped this case would demonstrate the RFU’s leadership in addressing sexism and misogyny within rugby.
“Instead, it has highlighted areas where further development of policy and process may be required.”
The RFU council – famously described by then England captain Will Carling in 1995 as “57 old farts” – has unpaid positions but they come with hospitality benefits which, for England men’s Tests, are worth several hundreds of pounds for each fixture.
In response to the letter, RFU president Deborah Griffin said: “I can assure you that the disciplinary process relating to this case was both robust and independent.
“While due process matters, so too does what we do next. We are not standing still on this issue.
“We are taking deliberate action to strengthen how we address sexism and misogyny across the game and to ensure that our values are consistently upheld in practice, not just in principle.”