Ms Davidson said more than 550 teachers who had qualified outside Scotland were prevented from taking up posts because they could not be registered until they had retrained north of the border.
She raised the issue after the headteacher at Trinity Academy in Edinburgh appealed last week to suitably qualified parents for help in filling two vacancies for maths teachers.
In a letter to parents, Bryan Paterson wrote: “Where necessary, maths teachers may share some classes, particularly in S1 to S3, with colleagues from other faculties who have a mathematics background.
“Finally, if any parent can support us in any way, or knows anyone who might be able to do so, please contact me directly.”
Earlier this year a school in education secretary John Swinney’s Perthshire constituency made a similar appeal.
At first minister’s questions in Holyrood, Ms Davidson cited the case of a couple who moved to Scotland five years ago. The husband did his teacher training in maths and he worked for 15 years as a maths teacher in England.
Ms Davidson said: “When he moved here he was told he couldn’t teach maths any more without a full year’s retraining as a student. That is a qualified maths teacher not allowed to teach maths in Scotland. And he is not alone.
“We have a crippling shortage of teachers but according to evidence presented to this Parliament this year we have more than 550 qualified teachers from outside Scotland applying to teach here but who have been told by this government to go back to school themselves.”
However, the SNP leader rebuffed Ms Davidson, saying teachers who had qualified could now take up posts on a conditional basis as they worked towards becoming registered with the General Teaching Council for Scotland (GTCS).
Ms Sturgeon said: “I received that email as well yesterday (from the couple), so I have been able to look into it.
“The circumstances narrated in that email relate back to 2012. Since then … the General Teaching Council for Scotland has introduced provisional conditional registration. That individual, while he would not have been able to teach in 2012, may now be in a position to do so, which is why we will now be contacting that individual to see if he wants to take up a teaching post.
“That is a change in circumstances that frankly I’m quite gobsmacked Ruth Davidson didn’t bother to find out before she came here today.”
To date, Scotland’s secondary teacher vacancies have mainly been harder to fill in rural areas than cities.