The Russian Foreign Ministry said such an attack "blatantly violates" the U.N. charter.
Israeli warplanes struck deep in Syria Wednesday, Syrian officials said.
The Syrian government said a research facility was hit and others told of a weapons cargo being targeted. Two people were killed and five were injured, Syrian officials said.
The Arab League spokesman said the airstrike was a "glaring violation" of Syria's sovereignty.
Nabil al-Arabi, the Arab League's president, said the lack of international discussion in the past about Israel's bombing of Syrian sites "encouraged it to carry out the new aggression, taking advantage of political and security deterioration in Syria."
The Russian Foreign Ministry said if the airstrike information is confirmed "we are dealing with unprovoked attacks on targets on the territory of a sovereign country, which blatantly violates the U.N. charter and is unacceptable, no matter the motives to justify it,"
Israel officially had not commented on the airstrike.
"Clearly someone attacked something on the Syrian-Lebanese border," military expert Yossi Alpher said. "But it's extremely important in these situations that Israel does everything possible to avoid being accredited with these actions. There's a danger of retaliatory action, whether by Syria or Hezbollah."
Hezbollah pledged its solidarity with the regime in violence-torn Syria, saying Israel "perpetrated a barbaric attack."
The Syrian ambassador to Lebanon, Ali Abdul-Karim, said the government was keeping "the option ... to retaliate" on the table.
Iranian Deputy Foreign Minister Hossein Amir Abdollahian said the attack could have significant implications for Tel Aviv, which is within range of Hezbollah rockets.
In Washington, the White House, State Department and Defense Department would not comment.
The airstrike on the Syrian-Lebanese border followed reports of sorties by Israeli military planes, The Guardian said. U.N. forces on the Israel-Lebanon border "recorded a high number of Israeli overflights throughout the day and the night," U.N. spokesman Andrea Tenenti told the British publication.
U.N. Secretary-General Ban Ki-moon expressed "grave concern." He said international law and sovereignty must be respected and pleaded for "all concerned to prevent tensions or their escalation," his office said.
The Iraqi daily Azzaman, published in Baghdad, London and Beirut, Lebanon, quoted a Western diplomatic source as saying the Israeli attack actually took place more than 48 hours before it was reported Wednesday.