Legislation on paternity leave comes into force on April 3, giving new fathers the right to take six months off work.
But uswitchforbusiness.com said it found just 1% of SME owners think the new law will help their business.
Two-fifths apparently want the Government to exempt small businesses from having to fulfil the duty and around a third imply they will now discriminate against men whom they believe are prone to having a child in the near future: 32% of SME bosses say they would now think twice about the staff they employ.
The Treasury is reportedly considering such an exemption, meaning men working for businesses with a maximum 10 staff will have their new-found paternity rights removed. Making such an allowance for smaller companies may end up discouraging such firms from taking on more workers.
The website's James Constant said: "Our research shows that SMEs are prepared to change their hiring policy as a result of what many see as punitive new paternity leave rules."