"The Egyptian army deliberately fired at two positions belonging to Gaza's National Security apparatus near the strip's border with Egypt," Gaza's Interior Ministry said in a statement.
"The shooting came as a surprise, without any provocation from the Palestinian side," it added.
The ministry slammed the incident as a "dangerous precedent" and called for an investigation.
Earlier Tuesday, eyewitnesses said that a bomb had gone off near an Egyptian army patrol stationed near the Gaza border, prompting the patrol to fire on the Palestinian positions.
An Egyptian military source, for his part, denied that shots had been fired at any Palestinian border posts, insisting that the Egyptian army "has never done this and never will."
"If we did, we would announce it and state our reasons for it – but that's not the case here," he said.
The source went on to say it was not the first time for such accusations to be leveled against the Egyptian army by the Gaza authorities, describing the assertions as "unrealistic."