Mr Ouattara's party supported the changes but the members of the ruling coalition were opposed.
The strongest opposition came from the PDCI, which backed Mr Ouattara in the disputed November 2010 election.
Analysts say the splits highlight the continued political instability in the world's major cocoa producer.
It is slowly recovering from months of unrest following the poll, in which former President Laurent Gbagbo refused to accept Mr Ouattara's victory.
Kenya's controversial marriage reforms
PDCI candidate Henri Konan Bedie came third in the election and in exchange for his support in the run-off, Mr Ouattara appointed a prime minister from the PDCI.
But sources say Mr Ouattara feels he no longer has the full support of the PDCI, which governed Ivory Coast for 39 years from independence until a 1999 coup.
Like many African countries, Ivory Coast's law currently recognises the husband as head of the household, responsible for all major decisions - a situation Mr Ouattara's RDR wanted to change.
Amadou Gon Coulibaly, general secretary of the presidency, said the unexpected decision to dissolve the government came after the PDCI voted against the new marriage law on Tuesday evening.
"You can say that this was the drop of water that made the vase overflow," a presidential aide, who did not wish to be named, told the AP news agency.
Since assuming control in March 2011, Mr Ouattara has presided over an economic recovery in Ivory Coast.
But these economic gains have been threatened by a series of armed attacks on military targets and the country's infrastructure, allegedly launched by allies of Mr Gbagbo from neighbouring Ghana.
The border between the two countries was closed for two weeks after an attack on an army checkpoint in September.
Mr Ouattara has been accused of not working hard enough to promote national reconciliation between his supporters and those of Mr Gbagbo.
More than 3,000 people were killed before Mr Gbagbo was forced from office, with the help of France and UN troops.
Mr Gbagbo is now awaiting trial for crimes against humanity at the International Criminal Court in The Hague.
Ivory Coast President Alassane Ouattara has sacked his government in a row over a new marriage law which would make wives joint heads of the household.