Mueen Shadid also reports from Tulkarm that seven Palestinians, including a woman, were injured after Israeli soldiers opened fire at people at the checkpoint on Thursday.
Witnesses said Israeli soldiers wanting to search a Palestinian youth, asked him to remove his clothes. That was when he blew himself up, they added.
There was no immediate claim of responsibility.
One soldier was killed and at least two other Palestinians died, Israeli military sources said. Three Israeli soldiers were injured.
One Palestinian witness, who was hit by shrapnel himself, said:"I was standing by the checkpoint south of Tulkarm when I heard an explosion and then another explosion near an Israeli jeep at the checkpoint."
After the attack, the occupation army imposed closures on the West Bank towns of Tulkaram and Qalqiliya, preventing people from coming in and out.
Israel shelled the Gaza Strip on Thursday to enforce a new "no-go zone" designed to prevent Palestinians from firing rockets from the Gaza Strip, from which troops withdrew three months ago after 38 years of occupation.