The senior Hamas official was detained when troops burst into his home early on Saturday according to his wife, Huda.
Palestinian security sources said that 30 army jeeps entered the West Bank town of Ramallah early on Saturday morning and left immediately after Mr Shaer's arrest.
An Israeli army spokesman confirmed carrying out the arrest "as part of our fight against the radical Hamas movement," which refuses to recognise the Jewish state's right to exist and renounce violence.
Earlier this month, Israeli forces also arrested Aziz Dweik, the Hamas speaker of the Palestinian parliament.
As part of its crackdown against Hamas, which Israel and the United States consider a terrorist movement, the Jewish state on June 29 detained 64 other leading Hamas figures, including eight ministers and 26 lawmakers, in a massive sweep across the West Bank.
The Israeli crackdown, which has also involved large military incursions in Palestinian areas, began on June 28, three days after Palestinian militants from Gaza killed two soldiers and captured a third in a cross-border raid.
The military says it aims to recover the soldier and to stop Palestinian militants from firing rockets into Israeli territory.
Following the capture of the Israeli soldier, the Jewish state embarked on a campaign to strangle Hamas, whose armed wing was one of three militant groups which took part in the abduction.