She takes a newly created non-PR role at the DTI as director of business services. She reports to minister Nigel Griffiths and will carry out a review of the way the department supports small businesses.
Hewitt's role at 3i will be covered by worldwide marketing director Patrick Dunne, who takes the new title of group communications director.
He will oversee all external and internal communications, the press office, investor relations, public affairs and brand management.
Meanwhile, the marketing role will be given to global technology marketing manager Ali Erfan, who has been promoted to marketing director.
Latest figures show that 3i, Europe's biggest venture capital firm, has invested more than £15bn in the six months to the end of last September.
However, late last year the firm also announced a slump in investment returns, citing weak stock markets and tougher economic conditions.
The total return on investments had dropped by 14.4 per cent for the six months to the end of September, but this compared with a 28 per cent drop in the London stock market, the company pointed out.