One of the three, a 24-year-old woman, was killed, emergency services said.
In both incidents, the attackers were "terrorists," police said. The incidents came amid simmering tensions -- not just between Israel and Palestinians, but between rival Palestinian factions as well.
"The atmosphere of violence rides the wave of Palestinian incitement," Israeli military spokesman Lt. Col. Peter Lerner said on Twitter.
After the Tel Aviv stabbing, a Palestinian suspect from Nablus in the West Bank was arrested "with the help of eyewitnesses while he was hiding in an apartment building in the fourth floor nearby the central bus station," police spokeswoman Luba Samri said.
The victim, a member of the Israel Defense Forces, was taken to a hospital in serious condition, police said.
After the stabbings at the Alon Shvut junction in the West Bank, the attacker was shot by a security guard, police said.
The junction is the same site where three Israeli teens were kidnapped and later found dead, ultimately sparking an Israeli military campaign targeting Hamas in Gaza called Operation Protective Edge.
Fatah accuses Hamas of bombings
The incidents Monday -- the latest in a string of attacks -- came amid a new round of infighting
between Palestinian factions.
The political party Fatah said Sunday it will scrap a series of events to commemorate the death 10 years ago of Palestinian leader Yasser Arafat. The group blamed rival faction Hamas, saying it is behind a series of bombings at the homes of Fatah leaders.
Hamas denounced the attacks, according to the Facebook page of spokesman Sami Abu Zuhri.
Fatah controls the West Bank, and Hamas controls Gaza. While the parties have fought violent battles in the past, they've made repeated announcements of plans to form a unity government as well.
The 'auto intifada'
On Saturday, Israeli police shot and killed a Palestinian man who attacked police officers with a knife in a village in northern Israel, police said. There were conflicting accounts
of exactly what happened.
has been facing what some call an "auto intifada"
-- a spate of attacks on Jewish civilians in Jerusalem by Palestinians driving vehicles.
Hamas said it "blesses the action. What is happening in Jerusalem is pushing us to prepare for war."
Violence has recently involved the Temple Mount, the holiest site in Judaism and one of the three holiest sites in Islam.
It's known to Muslims as Haram al-Sharif, or the Noble Sanctuary, and Jews are allowed to visit the site but not to pray there.
A Palestinian recently shot and critically wounded a rabbi, Yehuda Glick, who campaigns for the right of Jews to pray at the site. After an Israeli counterterrorism unit shot and killed the assailant hours later, Palestinian Authority President Mahmoud Abbas
-- part of Fatah in the West Bank -- wrote to the assailant's family saying he would "go to heaven as a martyr defending the rights of our people and its holy places."