Israeli sources have suggested Shihadeh was the mastermind of last Thursday's deadly attack on a Jewish seminary in West Jerusalem although Islamic Jihad never claimed responsibility.
Palestinian security forces deny the allegations and say Shihadeh had adhered to a unilateral ceasefire with Israel.
Islamic Jihad condemned the assassination as a signal of Israel's lack of commitment to reaching a ceasefire and fired at least four rockets over the border on Wednesday in what it described as an "initial" response to the assassination.
The rockets hitting the border town of Sderot ended a week-long suspension of such attacks by Islamic Jihad.
An Israeli military spokesman said a house was damaged but there were no casualties.
Earlier in the day, Israeli forces killed another Islamic Jihad activist, this time in Saida near Tulkarem in the northern West Bank.
Israeli forces exchanged fire and killed Saleh Karkour, 27, then demolished part of the house where he was staying.
Israel's controversial policy of assassination is condemned by international human rights organisations as illegal.
Some even call it extra-judicial execution.
Israeli forces also carried out raids in several other towns in the West Bank on Wednesday.
Residents of these towns and surrounding villages reported that Israeli forces had detained at least 12 Palestinians, Al Jazeera's Nour Odeh reported.
In Qalqiliya, the Israelis were involved in a large military operation, deploying in all its neighbourhoods to conduct random searches of residents' homes.
Al Jazeera boycott
In a separate development, Israel has decided to boycott Al Jazeera over what it called biased coverage of events in the Gaza Strip, according to an Israeli radio station.
The Israeli foreign ministry was reportedly sending a letter to Al Jazeera intimating its decision, but there has been no official confirmation.
Walid al-Umari, Al Jazeera's Palestine bureau chief, said the decision was part of a campaign against the channel, backed by Israel's foreign ministry.
"A state that respects the freedom of expression or claims that it is democratic should not limit the movement of press teams," he said.
"I dare any Israeli official to bring up what they call incitement or lies reported by Al Jazeera. What we reported were real facts on the ground."
Israeli officials will stop giving interviews to Al Jazeera's correspondents, who will also not be allowed to enter government departments, the radio station said.
In a statement released on Wednesday evening, Al Jazeera said it was very surprised to hear the Israeli radio broadcast, and that it had not received any formal communications from the Israeli government.
Al Jazeera reiterated that it has always endeavoured to cover the news in a fair, balanced and professional manner, and will continue to report from all over the world in accordance with the highest journalistic standards.