Donald Trump's running mate, a long-time opponent of Planned Parenthood, will be sent a gift certificate for every donation.
The campaign began in 2011 when as an Indiana congressman he introduced several anti-abortion measures.
They included the first bill to strip the provider of all federal funding.
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In March this year, as Indiana governor, Mr Pence signed an anti-abortion bill that is seen as one of the most restrictive in the US, barring abortion in Indiana on the basis of disability, gender or race of the foetus.
Parts of that law were blocked by the courts, but not until after a social media backlash which saw women phoning or tweeting Mr Pence details about their menstrual cycles under the hash tag #periodsforpence.
There had already been a significant rise in gifts to the country's biggest abortion provider in the wake of Mr Trump's election last week.
But then over the weekend, many women went on social media to say they had made a donation in Mike Pence's name.
Mike Pence's anti-abortion stance mirrors that of President-elect Trump, who wants to cut funding to Planned Parenthood, and who has in the past said women should be punished for undergoing an abortion if it were made illegal, though he later withdrew the statement.
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Planned Parenthood hasn't commented in detail on the post-election trend of donating in Mr Pence's honour.
But the organisation said on social media they had been "blown away by the support" and acknowledged that many people are donating in both Mike Pence's and Hillary Clinton's names.
The vice president-elect has so far not commented on being the nominal donor of thousands of dollars to the organisation.

Almost 1.7m euro (£1.3m) has been paid out by the Erne Trust since 2012.
The money was for legal bills and other fees incurred by the Quinn family.
The receiver for the assets of various Quinn family members took legal action to have the trust's donors disclosed to him.
He suspects it is a "sham trust", which is a conduit for assets which have been concealed from him.
Declan Taite was appointed receiver in 2012 at the request of IBRC, formerly known as Anglo-Irish Bank.
He told the court that it is his job to identify, locate and collect assets.
He added that the Quinn's have "openly admitted" they put property assets beyond the reach of IBRC and that those assets have "generated tens of millions of euros".
He said he is trying to "understand the provenance" of the money in the trust to determine that it does not originate with the Quinn family.
A list of donors including names, addresses and sums donated has now been given to Mr Taite.
His barrister said the close family connections includes siblings, however, a barrister for the trust said he was "not aware" of a sibling connection.
The trust's barrister added that it was "not surprising" that Mr Quinn's business acquaintances should support him.
Mr Taite's barrister said that having received the list of names there may now be a need to gather further affidavit evidence.
The case was adjourned until September.
Donations to US family planning organisation Planned Parenthood in the name of Vice President-elect Mike Pence have surged.
[NEXT_CONCEPT]
The donors who have effectively been paying Seán Quinn's legal bills include business acquaintances and "close family connections", the High Court has been told.