The accident, which involved a white Vauxhall Astra van, happened on the A701 Howden Hall Road in Kaimes at about 07:50.
The woman was taken to Edinburgh Royal Infirmary.
The road was closed between Alnwickhill Road and Burdiehouse Road but has since reopened. Police appealed for anyone with information to contact them.

Bournemouth's 3-2 win over Swansea on Saturday leaves them 13 points clear of the Premier League drop zone.
And the club's third successive league win has helped wipe away any relegation fears from the supporters.
"Everyone around us [thinks we are safe] and the fans I heard are singing 'we are staying up'," said King.
"But our mentality will not see us take the foot off the gas and relax now," he told BBC Radio Solent.
"We do not stop just because everybody from the outside thinks we are safe."
The 24-year-old scored his second goal in as many matches against Swansea to take his tally to five for the season.
King, who joined the Cherries after leaving Blackburn in the summer, admits he is beginning to feel at home thanks to Bournemouth boss Eddie Howe.
"The last few months have been amazing and I have learnt a lot from the manager," continued King.
"It's not been easy moving house, moving friends and everything.
"I was used to being in one place - in Manchester for seven years - but I am loving life and football at the moment, things are going well for me and especially for the club."

The union is supporting a campaign to stop Bangor University student Shiromini Satkunarajah being deported to Sri Lanka.
The 20-year-old has been taken to a detention centre after being refused asylum.
The Home Office said it considers each case carefully.
Miss Satkunarajah, who was born in Sri Lanka but has lived in the UK for eight years, is due to finish her electrical engineering degree this summer.
She was arrested on Tuesday and taken to a detention centre to await deportation on 28 February.
Thousands of people have signed a petition to stop her deportation.
NUS Wales deputy president Carmen Smith told BBC Wales: "We want the home secretary to stop the callous and inhumane deportation of Shiromini.
"She doesn't have any family or friends in Sri Lanka. Wales is her home.
"She has three months left of her degree. It's a brutal thing to do at such a time in her educational experience."
Arfon MP Hywel Williams said the UK government should use "common sense" in dealing with Miss Satkunarajah's case.
"She has three months to go before she graduates in a field where we really do need people and she's an excellent student," he said.
"There is a certain amount of discretion they can operate and I really wish they would."
A Home Office spokeswoman said: "We do not routinely comment on individual cases.
"The UK has a proud history of granting asylum to those who genuinely need it and every case is carefully considered on its individual merits."
A 19-year-old woman has been seriously injured after being hit by a van in Edinburgh.
[NEXT_CONCEPT]
Bournemouth striker Joshua King insists the Cherries will not lose focus on the rest of the season after their priceless win over Swansea City.
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Any student seeking asylum should be able to finish their education here, the National Union of Students (NUS) Wales has said.