The situation in Calais showed “a system that is breaking down”, he told BBC Radio 4's World This Weekend, adding: “I see a country who don't want to take the responsibility that they should”.
Migrants in Calais are making nightly bids to cross the Channel.
The UK and French governments have announced they will bolster security around the Eurotunnel site in Calais.
Mr Johansson was critical of Mr Cameron's rhetoric: “I hear what he is saying about 'illegal immigrants' and 'swarms' and I think he is trying to divide people, that that is not a constructive way.”
Speaking to BBC Radio 4's The World This Weekend programme, Mr Johansson criticised Mr Cameron for using the word “illegal” about asylum seekers before they have been through asylum the process, and said they were seeking a basic human right.
Sweden was currently accepting around 1,000-1,200 asylum applicants a week, Johansson said.
Since 2013, Sweden has thrown its doors open to Syrians, granting them near automatic residency and boosting overall asylum applications — the highest per capita in the EU according to Eurostat — to record levels.
Last year Sweden accepted 30,000 asylum seekers compared to the UK's 10,000.
Thousands of migrants have attempted to access the Eurotunnel terminal in the last week, and nine have died trying to access the tunnel since the start of June.