All three statements expressed concern at the timing and manner of the action, coming just weeks before presidential and legislative elections set for February 16. Chief Justice Walter Onnoghen would have ruled on any dispute in the elections.
But on Friday Buhari suspended him, pending the resolution of a corruption trial at the Code of Conduct Tribunal.
He said he took the decision in compliance with a ruling by the tribunal -- a ruling that Onnoghen is challenging.
"The decision to suspend the Chief Justice has led to many Nigerians, including lawyers and civil society observer groups, to question whether due process was followed," said a statement from the EU Election Observation Mission (EU EOM).
"The timing, just before the swearing in of justices for Electoral Tribunals and the hearing of election-related cases, has also raised concerns about the opportunity for electoral justice," it added.
"The EU EOM calls on all parties to follow the legal processes provided for in the constitution and to respond calmly to any concerns they may have," it added.
Buhari, who came to power in 2015 on a pledge to fight corruption, is seeking a second term.
The US embassy also said it was "deeply concerned" at the decision to replace Onnoghen "without the support of the legislative branch on the eve of national and state elections".
The British High Commission also expressed "serious concern over the suspension".
It added that "the timing of this action, so close to national elections, gives cause for concern.
"It risks affecting both domestic and international perceptions on the credibility of the forthcoming elections".
Nigerian lawyers and opposition parties have already condemned the suspension.
Onnoghen was charged on January 12 for false declaration of assets, after millions of cash in local and foreign currencies were allegedly traced to his accounts.
Buhari also accused him of frustrating the war against corruption by freeing graft suspects before his court.
He has replaced him with Justice Ibrahim Tanko Mohammed, who was his second-in-command.