Emergency services were called to an address in Pattison Street in Leith following reports of a substance spilling in the fourth floor of a flat at around 3.30pm yesterday.
A Police Scotland spokesman for the Lothians and Scottish Borders Division refused to describe it as a chemical incident but could comment no further about what was discovered.
They said a member of the public had initially contacted the ambulance service concerned they may have come into contact with a hazardous substance.
While residents living near to the block were evacuated, a spokesman said there are "no health concerns for any other individuals who were in the address".
Four firefighters wearing what appeared to be hazard protection suits were seen entering the building as police maintained a cordon.
A woman was taken to the Edinburgh Royal Infirmary and it is believed her young child who was at the address at the time was being looked after by relatives.
Meanwhile, police in Dumfries are dealing with an incident at a house.
Officers have sealed off the area around Syme Road
Police would only say there is an ongoing incident. Local people tweeted an image of an ambulance arriving through a cordon.
A Police Scotland spokesman said: "The area has been cordoned off to ensure the safety of public in the area and to allow police to carry out their duties in a safe environment. A full update will follow at the conclusion of the incident."