The attack took place at the offices of the Swedish Federation for Lesbian, Gay, Bisexual and Transgender Rights (RFSL) on Sveavägen just after 3.30pm.
Police arrested a man around fifteen minutes later in connection with the incident. He was still carrying the axe when he was apprehended.
RFSL chairman Sören Andersson has confirmed that woman was an employee of the organization. He is in no doubt that the crime was motivated by hatred.
"It's obvious that this can't be anything other than a hate crime directed at our organization," he said.
"This clearly shows that the work done to counteract hate crimes has not been sufficient. More needs to be done. It is dreadful, really dreadful, when staff cannot feel safe at work," he added.
The woman has been taken to hospital where her injuries are not reported to be serious.