Scottish Liberal Democrat leader Willie Rennie pressed her on the rise as he also complained the equivalent of just 7.5 additional staff have been taken on to help officers deal with call-outs involving people in mental distress.
Mr Rennie raised the issue at First Minister's Questions, demanding the SNP leader stops "pontificating about other parties and her referendum" to deal with the issue.
He claimed a survey of police staff by the Scottish Police Authority, which is expected to ask officers about morale in the force, has been delayed for three years "making people suspicious that it is going to be bad news".
With no survey available, he said Liberal Democrats had uncovered "shocking" figures showing "the number of working days lost to mental ill health has gone up 11% in just two years for police officers, for police staff it is 25%".
He went on to state that while the Scottish Government had pledged to recruit mental health staff to work alongside police officers, his party found "this adds up to a miserable seven-and-a-half extra staff".
Mr Rennie said: "We have police off sick, massive demands on their time. Just seven-and-a-half extra staff to help them.
"Will the First Minister take off time from pontificating about other parties and her referendum and take practical action to increase mental health support for our police?"
Ms Sturgeon insisted her Government is investing both in policing and improved mental health services.
She said: "These are important issues and that is why we are investing in our police service, we are investing in mental health support workers across a range of different settings.
"We made a commitment to do that over this Parliament and we are delivering that commitment over this Parliament."
She told Mr Rennie she would write to him about the police staff survey, but said overall police - like other pubic sector workers - "clearly do jobs that are incredibly stressful".
She insisted the "welfare of police is very important" as she told how the SNP had increased officer numbers since coming to power.
With officers in Scotland also awarded a 6.5% salary increase, Ms Sturgeon said her Government is "ensuring our police officers are properly rewarded for the job they do, through a pay increase that is much greater than elsewhere".
Police Scotland Deputy Chief Constable Fiona Taylor said: "The wellbeing of our officers and staff is a priority and we have a range of support mechanisms in place.
"An engagement and wellbeing survey will be carried early next year. Response rates in the previous two surveys were lower than we had hoped for and we will be taking time to encourage as many people as possible to take part in the next one.
"In the meantime, we will continue to work closely with all our staff associations."