Loud bangs were heard coming from the Scottish Police Services Authority's premises at Howdenhall Road in the south of the city just after midnight.
A masked man who was seen running from the scene escaped in a car, driven by another man, at St Katherine's Brae.
The fire brigade put out two fires in offices on the ground floor but there has been extensive smoke damage throughout the building.
The man who was seen running from the scene is about 5ft 6in, of thin build, and was wearing a dark top, possibly hooded, and a dark mask.
About a fifth of all Scotland's forensic science work is carried out in the laboratory and managers are now assessing the impact on current casework from fire, smoke and water damage.
Tom Nelson, Scottish Police Services Authority's director of forensic services, said: "This has been a serious incident, but one that I am pleased to say has not resulted in any injuries to my staff.
"An initial assessment suggests that although there has been extensive smoke damage throughout the building, only two rooms have suffered from fire. Neither of these rooms are key scientific laboratory facilities."
A Lothian and Borders Police spokesman said: "We are appealing for anyone who was in the area of Howdenhall Road or St Katherine's Brae at the time of the incident, who noticed any suspicious activity, to get in touch with us immediately.
"Similarly, we want to hear from anyone who saw a vehicle being driven at speed in the area in the early hours of this morning.
"Anyone else who has
any other information that can assist our inquiries should also get in
Source: BBC News
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