Arter damaged his Achilles during Bournemouth's 2-0 win over Southampton while O'Shea was taken off during the first half in Sunderland's 2-all draw with Crystal Palace.
Ireland manager Martin O'Neill will hope both are available for the friendly matches against Switzerland and Slovakia at the end of the month.
Tipperary’s Shane Long damaged his knee during the Saints loss at the Vitality stadium but manager Ronald Koeman says the Gortnahoe native's injury is not that serious.
