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.