Mr Evans is taking leave due to a stress-related illness.
He was appointed as chairman at M&G in October 2018 ahead of the separation of the firm from former parent group Prudential.
He was also formerly chairman of Hargreaves Lansdown.
Ms Clutterbuck joined the board of M&G as senior independent director in October 2020. She is also chair of Paragon Banking Group and non-executive director of Nordic financial services group Sampo.
She was previously on the board of Hargreaves Lansdown.
She has spent over 30 years in financial services including head of strategy, corporate development and communications at Pearl/Phoenix Group from 2008-2018. She was also previously head of financial institutions advisory at ABN AMRO Investment Bank and global co-head of the financial institutions group at HSBC Investment Bank.
Clare Thompson, the investment managers audit committee chair, will take on the role of interim senior independent director.