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The woodland park is popular with walkers and has views of the nearby Pentland Hills.
The Scottish Fire and Rescue Service said it sent two fire engines to the area to support the search.
Two ambulances, a special operations team and a critical care paramedic from the Scottish Ambulance Service also attended.
Colin Beattie, the MSP for Midlothian North, said it was a "deeply distressing" incident for the local community and that many people would be shocked and saddened by the news.
He added: "However, with a Police Scotland investigation ongoing, it would be inappropriate to comment on the circumstances surrounding the incident.
"I would urge people to respect the privacy of the family and their loved ones at this extremely difficult time, and to allow the police the space they need to carry out their inquiries."
Gore Glen was the site of Scotland's first industrial-scale gunpowder mill, which was established in 1794.
For nearly 70 years, the Gore Water was used to power 10 waterwheels.
