At 0552 GMT, the rand was 0.07 percent weaker at 14.0525 per dollar compared with the previous close.
Cash-strapped Eskom implemented some of the worst-planned blackouts in years last week, shaking confidence in South Africa's ability to power the continent's most industrialised economy and hitting the rand.
Mboweni is expected to announce a bailout for the utility, which supplies 90 percent of South Africa's power and has government guarantees for most of its 420 billion rand ($29.86 billion) in debt, in his budget speech which kicks off at 1200 GMT.
Standard Bank rand trader Warrick Butler said how the plan for Eskom is received by credit ratings agencies, particularly Moody's which is the only one to maintain an investment-grade rating for South Africa, will be key.
"Will this budget be a stretch too far for them? Who knows, but I for one am a little worried," he wrote.
Before the budget, at 0800 GMT, South Africa's statistics office, Statistics South Africa, will also publish consumer price inflation and core inflation data.
Government bonds were also flat, with the yield on the benchmark government paper due in 2026 easing 0.5 basis points to 8.870 percent.