The warning came as UN and humanitarian workers condemned an airstrike by the Saudi-led coalition targeting Yemen's Shia Houthi rebels that reportedly killed at least 15 civilians near the port city of Hodeida.
Video footage released by the Houthis showed a mangled minibus littered with groceries and a woman's handbag, with rebel officials saying a day earlier that the airstrike in the Jebel Ras area had also wounded 20 others.
The Houthis said five members of the same family were killed in the vehicle, adding that many women and children were among the casualties.
Eyewitnesses said the attack appeared to target a rebel checkpoint in the area.
"The United Nations agencies working in Yemen unequivocally condemn the attack on civilians and extend our deepest condolences to the families of the victims," Grande said.
"Under international humanitarian law, parties to the conflict are obliged to respect the principles of precaution, proportionality and distinction," she said. "Belligerents must do everything possible to protect civilians - not hurt, maim, injure or kill them."
Hodeida, with its key port installations that bring in UN and other humanitarian aid, has become the centre of Yemen's conflict, with ground troops allied to the coalition struggling to drive out the rebels controlling it.
The UN in Yemen says that since June more than 170 people have been killed and at least 1700 have been injured in Hodeida province, with more than 425,000 people forced to flee their homes.