Aleena Rafi, an unpaid special constable, appeared in a YouTube video to talk about her short time with the force.
She is the first recruit to adopt the head covering, which was introduced as part of the uniform in 2016.
A link to the video on Twitter, which was posted last week by Police Scotland, has received dozens of abusive comments.
Speaking in the video, Ms Rafi said: “So far I’ve really enjoyed myself and when I’ve been out, the public have been really welcoming. I have loved my time so far and hope to experience more new things with the police.
“I only realised after I joined that I was the first hijab-wearing officer in Scotland. For me to hear that, I was quite shocked and I was proud as well.
“Wearing the hijab is, for me, a part of my life so when I was thinking of joining Police Scotland, it did play an integral part in me deciding whether this is what I wanted to do.
"The fact that Police Scotland has a hijab as part of the uniform made the decision easier for me...out on the beat, the hijab does grab people’s attention, but for me I’m used to be the odd one out or the one who’s different so I don’t really look at that as being a negative.”
In a comment posted on Twitter after the online abuse was highlighted, the Scottish Police Muslim Association said: “We have the pleasure of knowing Aleena...she is part of our team and is a fabulous, strong willed, formidable and dedicated young woman...an asset to the force who will no doubt make an impressive special constable. Backing her all the way.”
Ms Rafi also received the support of justice secretary Michael Matheson, who said: “Special Constable Rafi is right to be proud to be the first officer to wear a hijab.
“Police Scotland recruit special constables based on their commitment, enthusiasm, common sense, confidence, a mature approach and great interpersonal skills.
“That is what matters and there is simply no place in Scotland for these types of negative comments.”
Police Scotland introduced the hijab after figures showed there were just 127 applications from black and Asian candidates in 2015/16 – 2.6 per cent of the total number of people applying for a job with the national force.
In a briefing to the Scottish Police Authority (SPA) at that time, the force said it would need to recruit an additional 650 ethnic minority candidates to reflect the 4 per cent of those from black and Asian backgrounds in society as a whole, something it described as “unachievable”.
While just 4 per cent of the Scottish population comes from a black or Asian background, the figure rises to 12 per cent in Glasgow and 8 per cent in Edinburgh.
While there is no ban on female officers wearing headscarves, those wanting to do so must get permission from their line manager. No such authorisation is be required for those wanting to wear the standard issue hijab.
Under Police Scotland guidelines, religious symbols such as crucifixes and the Sikh kara and kirpan can be worn if done so discreetly below the uniform.