Assuming we're allowing past governments - at the beginning of 2011, the second Merkel Cabinet (Germany) included twelve ministers with PhDs or other doctoral degrees.
Unfortunately, only ten still retain their degrees, as in February 2011, Karl-Theodor zu Guttenberg's doctorate was withdrawn by the University of Bayreuth after plagiarism was discovered (see Guttenberg plagiarism scandal). A couple of years later, the University of Düsseldorf revoked Annette Schavan's doctorate for the same reason.
Nevertheless, at the beginning of 2011, twelve out of sixteen ministers held doctorates.
||Federal Minister for Foreign Affairs
||Federal Minister of Economics and Technology
|Thomas de Maizière
||Federal Minister of the Interior
||Federal Minister of Finance
|Ursula von der Leyen
||Federal Minister of Labour and Social Affairs
|Karl-Theodor zu Guttenberg
||Federal Minister of Defence
||Law (revoked in 2011)
||Federal Minister for Family Affairs, Senior Citizens, Women and Youth
||Federal Minister of Health
||Federal Minister of Transport, Building and Urban Affairs
||Federal Minister for the Environment, Nature Conservation, and Nuclear Safety
||Federal Minister of Education and Research
||Philosophy (revoked in 2013)