MSCI's broadest index of Asia-Pacific shares outside Japan lost 0.3 percent. South Korea's Kospi dipped 0.3 percent.
Japan's Nikkei rose 1 percent thanks to a weaker yen, which fell to a three-week low against the dollar after the minutes were published.
The minutes of April's policy meeting noted Fed officials said it would be appropriate to raise interest rates in June if economic data points to stronger second-quarter growth as well as firming inflation and employment.
Such views helped revive the prospect of a rate hike in June, which had recently been dismissed by many investors.
Following the minutes, traders projected a 34 percent chance the Fed would raise rates in June, up from 15 percent on Tuesday, according to CME FedWatch.
Traders see a more than 50 percent chance of rates rising in July.
The dollar index hovered just below a seven-week high of 95.27 scaled overnight, boosted by sharply higher U.S. Treasury yields. The benchmark 10-year Treasury note yield jumped more than 10 basis points on Wednesday.
The greenback was steady at 110.090 yen after rising to a three-week peak of 110.250 overnight. The euro was pinned down near $1.1214, its lowest since late March.
"The dollar may well take a bit of a pause here as we have the (Federal Reserve) vice chairs speaking tonight. We suspect a lack of commentary on markets will be taken as a tacit endorsement of June re-pricing," wrote strategists at ANZ.
Fed vice chairs William Dudley and Stanley Fischer are due to speak later in the session and the markets will be eager to gauge their views on monetary policy.
Elsewhere in currencies, the pound was on a bullish footing after a poll gave the "In" camp, which supports Britain remaining in the European Union in a referendum next month, a substantial lead.
Sterling was close to $1.4636, a two-week high touched on Wednesday.
The stronger dollar weighed on commodities such as oil, which saw U.S. crude futures lose 0.4 percent to $48.00 a barrel. A stronger dollar tends to put non-U.S. buyers of greenback-denominated commodities at a disadvantage.
Three-month copper on the London Metal Exchange fell to as low as $4563.50 overnight, the weakest since Feb. 19.