A safety needle assembly includes a cannula connected to a hub, and a protector positioned over and covering the cannula. The protector is provided with an opening and is axially movable between a covering position and an uncovering position. A sheath provided with a channel is pivotally mounted with respect to the hub and is positioned in an initial position in which the through opening in the protector is closed by the sheath. The sheath is adapted to be pivoted away from the cannula towards an intermediate position and is adapted to be pivoted back towards the cannula to a cannula covering position in which the cannula is located within the channel. An engaging part of the protector engages the sheath during movement of the protector from the covering position to the uncovering position to cause the sheath to automatically pivot away from the initial position.