The Dow Jones closed at 18,116.04, down 105 points, or 0.6%, while the broader S&P 500 dropped 13 points, or 0.6%, to 2091.5.
The tech-heavy Nasdaq fell 16 points, or 0.3%, to 4,994.73.
The dollar rose against the euro by 0.2% to â‚¬0.9154.
The dollar's rise can hurt large US companies' profits, as they get less from their overseas earnings after currency conversions.
Additionally, the dollar's strength makes it harder for companies to compete with foreign rivals, which may be able to offer similar products more cheaply.
There was some welcome economic data on Tuesday, which showed US consumer prices had rebounded in February, but this failed to lift Wall Street.
The Consumer Price Index rose by 0.2% last month, after fuel prices increased for the first time since June.
The monthly rise follows three consecutive months of declines, including a 0.7% drop in January. On an annual basis, prices in February were unchanged from a year earlier.
Analysts said investors were wary of shares because of the possible impact of the stronger dollar on companies' profits.
"Right now, we are a bit of in a waiting pattern and the big news is going to be when these earnings reports start to hit in April," Peter Jankovskis, co-chief investment officer at OakBrook Investments, told Reuters.
(Close): The main US share indexes all fell on Tuesday as investors continued to fret about the effect of the strong dollar on corporate results.