At a press conference in Edinburgh, Ms Davidson said the SNP leader now had “no mandate, no majority and no cause” to hold another vote on the issue, and any claims to the contrary had been “utterly shredded”.
Ms Davidson was speaking after the Tories recorded their best-ever Holyrood result by securing 31 MSPs to overtake Labour while the SNP took 63 of the 129 seats, failing to win a second overall majority.
Speaking at the Apex Hotel in Edinburgh’s Grassmarket, Ms Davidson said: “As I said during the election campaign, the SNP manifesto does not give Nicola Sturgeon a mandate for a second independence referendum.
“Now that she has failed to win a majority, whatever claims the SNP were pursuing with regard to constitutional brinkmanship over the next five years have now been utterly shredded.
“No mandate, no majority, no cause - the SNP must now let Scotland move on.
“There has been a material change. As she starts her new term of office, I hope Nicola Sturgeon makes it clear that she will now focus entirely on what she was elected to do - lead a devolved administration.
“She should give families and firms the certainty they need. Nicola Sturgeon has it within her power to do that.
“I urge her to start this new parliament by ruling out another referendum.”
Prime Minister David Cameron earlier congratulated Ms Davidson on the ‘’historic result’’, saying she would ‘’stand up to the SNP and give Scotland strong opposition’’.
Among the party’s major gains was Ms Davidson winning the Edinburgh Central constituency from the SNP and deputy leader Jackson Carlaw taking the Eastwood constituency on the outskirts of Glasgow from Labour’s Ken Macintosh.
Two Tory MSPs were elected in Glasgow, where academic Adam Tomkins and food retail manager Annie Wells picked up seats.
The SNP’s Dennis Robertson lost his Aberdeenshire West seat to the Conservatives while Oliver Mundell - son of the Scottish Secretary - captured the Dumfriesshire constituency from Labour.
The Tories’ previous best result at Holyrood was 18 MSPs, a total the party achieved in both 1999 and 2003.
Ms Davidson congratulated Ms Sturgeon on the SNP victory but said the lack of a majority government was “very welcome and good for our democracy”.
She said: “Majority government has not worked well - too often over the last five years the SNP pushed through its agenda not on the strength of its case, but simply on strength of numbers.
“As a minority administration, I believe the SNP will be forced to listen, to learn and to improve.
“I am very very proud that our performance last night has helped to bring this about.”