The monthly report said equity funds saw most of the outflow with the £2.8 billion redeemed accounting for a 0.51% fall.
UK equity funds accounted for £1bn of this, followed by European equity funds which had an outflow of £813m and global equity funds with an outflow of £386m.
Asian equity funds had outflows of £191m, North American had £186m leaving, and Japanese equity funds saw the lowest outflow at £131m.
It was property that was hardest hit relative to the total size of the asset class, with outflows of £1.4bn meaning a 5.7% drop. Mixed Asset funds also recorded a relatively small outflow of £191m.
Despite this, total funds under management rose to £948bn at the end of June.
This situation was helped by fixed income funds receiving a net retail inflow of £258m, the fourth consecutive month of positive retail flows, and money market funds posting net retail sales of £157m.
The IA’s interim chief executive Guy Sears said: "The retail outflow in June occurred in the context of record levels of funds under management, and represented just 0.37% of total assets during a period of intense market volatility. Clearly, Brexit has been unsettling, with property and equity funds particularly affected following earlier outflows during 2016. At the same time, flows were positive into fixed income and targeted absolute return sectors as investors sought safer harbours."
"In the first six months of this year, industry funds under management grew by £22.6 billion,” Sears continued. “Fixed income funds saw the largest growth in funds under management in the year to the end of June with £13 billion. Funds under management in mixed asset funds increased by £5.2bn and equity funds grew by £1.4bn."