Officers have cordoned off a street at the top of Leith Walk near a convenience store.
Images posted on social media at around 6am this morning show a U-Save shop within the police cordon, which is situated on the corner of Montgomery Street and Elm Row.
One report on social media said a large police presence and an ambulance was spotted outside the store at around 10pm on Wednesday night.
It is not yet known the circumstances surrounding the incident. Police Scotland have been contacted for a comment.
We’ll bring you more on this breaking news story as we get it.
Join our Facebook group Our Edinburgh to share images and news from and around the Capital
Know someone that makes a difference in our community? Nominate them for a Local Hero Award HERE