Mr Parnaby, 30 years with the company, is said to be "retiring from the group to seek new opportunities".
Standard said Mr Parnaby had "contributed a great deal to the business", working across Standard Life Investments, the UK business, Europe and latterly responsible for growth in Asia.
The group said: "Standard Life has made good progress within its Asia and emerging markets business, including new branches opening for business in Singapore and Dubai and increasing our market shares in India and China. Our priority is to make sure we are set up to capitalise on the opportunities available."
Standard says the focus will now be on the development and expansion of retail savings and investments. "We will transition some key shared functions to a regional hub in Hong Kong, to move resources closer to the regional branches and customers."
Mr Parnaby will be replaced by Alan Armitage, reporting to Sandy Begbie who will assume group executive responsibility for the business unit.
The team supporting Standard's joint ventures in Asia will become part of the central strategy team.