Hussey will be away for just over a month, returning in mid-July after the NatWest Challenge.
"Dale's experience has been hugely beneficial," said Durham coach Martyn Moxon while adding that Benkenstein was the unanimous choice to take on the captaincy.
Benkenstein who is in the first season of a three-year deal with Durham has delighted his new employers with fifties in both the Championship and National League this year.
"Mike's left us in a great position and I'm hoping that we can continue to play positive and confident cricket while he is away," said Benkenstein of his new role.
Having won their first four Championship matches in emphatic style, Durham were held to a draw by Yorkshire in their last outing.