Muscat, speaking at a news conference on Wednesday, said all member states must be ready to share the burden of a further influx of migrants and asylum seekers.
"So far, Italy has had to take the brunt of this and that is not fair. One member state cannot tackle this crisis on its own and we can't leave Italy or another country to do that."
He told reporters in Strasbourg that solutions to the crisis "will not be easy" and called for a "fast track" process for "genuine" asylum seekers to enter Europe.
Muscat was speaking after he addressed MEPs in a plenary session in which he focused mostly on the migration crisis and called on the EU to reach a deal with Libya to stem the flow of irregular migrants crossing the Mediterranean.
Muscat warned that the 2015 refugee crisis had caught Europe off guard and that the EU must reach a deal with north African countries before next spring.
"The EU-Turkey deal may not be a perfect deal and is not a long-term solution, but it has made a difference," he said, referring to the EU's deal with Turkey to stem flows of migrants to Europe.
"Europe cannot be caught in this conundrum once again. Next spring, Europe will face a new heavy influx of migrants through the central Mediterranean. The reasons why such people undergo risky voyages are different from those forcing Syrian refugees to cross the Aegean Sea," he said.
"There is no doubt that unless the essence of the EU-Turkey deal is replicated in the central Mediterranean, then Europe will face another crisis."
Muscat sought to use Malta as an example on solidarity on migrant relocation, in that it has agreed to take in 131 migrants from Italy and Greece under an EU system.
"Malta had been left almost alone for many years, trying to overcome a migration crisis that was not our making. The only solution we were given was some more money.
"When the Council proposed the relocation system, some voices back home told me to stand back, arguing that no one had helped us when we needed help.
"It would have been a very popular stand with the silent majority, yet we opted to do just the opposite because we know that this is an issue of precedence and credibility. Solidarity is not à la carte, to be used when we need it and turn a blind eye when others need it, but is an essential a European value at the core of what the founding fathers envisaged 60 years ago."
However, Greens/EFA group co-Chair Philippe Lamberts questioned how Muscat hopes to reach a deal with Libya when it is still run by two "bellicose and rival" governments.
"This is not in line with European values," he warned.
Lamberts also accused Malta of acting as a tax haven for multinationals and "siphoning €4bn in tax income from other member states every year."