The country is moving in a positive direction, however, she urged the public to be “sensible” about the virus.
Her comments come as Scotland’s coronavirus restrictions are set to be eased further this weekend as self-isolation requirements will be scrapped.
Scots will instead be advised to “stay at home” if they are unwell, according to Scottish Government guidance.
New guidance said those with symptoms no longer need to take a PCR and mass testing will end from April 30 as testing sites close and contact tracing ends.
Speaking during a campaign visit to the Barrowfield Community Centre in Camlachie, Glasgow, the First Minister said: “It’s not the end of the pandemic. I think we’ve got to be clear that this virus is still with us.
“We see in other parts of the world it’s still causing a lot of problems and case levels here in Scotland remain high. The pressure on the National Health Service is still significant.
From May 1, the Scottish Government has advised that symptoms of the virus are considered to be: continuous cough; high temperature, fever or chills; loss of, or change in, your normal sense of taste or smell; shortness of breath; unexplained tiredness, lack of energy; muscle aches or pains; unusual hunger; headaches; sore throat, stuffy or runny nose; and diarrhoea, feeling sick or being sick.
Ms Sturgeon did, however, say there was an opportunity for the public to be optimistic about the next phase of the pandemic.
She said: “I would ask people to still be sensible about this virus. If you’re in crowded places indoors, wear a mask to reduce the risk of transmission and if you become unwell, then stay at home for a few days.
“If we’re all sensible and, of course, if we avoid new variants, then there is every reason now to be a lot more optimistic about the period that lies ahead.”
Linda Bauld, a public health expert, told BBC Good Morning Scotland that Scotland is now treating the Covid-19 pandemic like any other virus – but issued a warning that the pandemic was not yet over.
And she said measures may need to be reassessed if a new variant “really challenged” the progress made.
The Edinburgh University professor said: “Essentially we are moving to a stage now where we are less worried about infection and what we’re focusing on is trying to find people who have the virus, who need support or are supporting those who are most vulnerable.
She added: “We’re kind of moving to a stage where we’re treating this a bit like other viruses which I know not everyone agrees with.
“(It’s) recognising that we’re at a different stage in the pandemic.”
The NHS will also be taken off an emergency footing from the end of Saturday.
However, Scots who work in health or social care sectors, those visiting hospitals and care homes, will still be able to access coronavirus testing.