Strods, a member of the nationalist For Fatherland and Freedom party, said he will leave his post on Tuesday after his party names a replacement.
"My family needs me more than ever before," Strods told reporters, but declined to give details. Local media have reported that his grandson is gravely ill.
Strods, 45, took office in October 2006 as a member of the four-party coalition government that was formed after parliamentary elections.
Rumors had been circulating for months that Strods' departure was imminent, but the minister denied any intention to leave his post, which plays a key role in distributing hundreds of millions of euros in EU development funds to Latvians.
Strods is the second minister to quit the 19-member coalition government.
The head of Russian Technologies, Sergei Chemezov, clarified the fate of anti-aircraft guided missiles that Russia was supposed to deliver to China
The Basmanny Court of Moscow arrested Michael Calvey, the founder of Baring Vostok investment fund, on allegations of embezzling 2.5 billion rubles from Vostochny Bank. Calvey will be held in custody until April 13