Corn was also set for a weekly gain but was down on the day as weather forecasts predicted drier weather that could help US farmers to accelerate planting after a slow start.
Soybeans were little changed on Friday, in keeping with a stable performance over the week, as traders weighed up large global supplies against US planting risks and robust weekly US exports.
The Chicago Board Of Trade's most active wheat contract was up 0.5 percent by 1146 GMT at $4.33-1/4 a bushel. This put it 2.9 percent up on the week, the biggest gain in 11 weeks.
"There is adverse cold weather for the US winter wheat crop reflected in the price action today," said Kaname Gokon from Tokyo brokerage Okato Shoji.
Low temperatures in north-central Kansas are expected to be in the mid to upper 20s (Fahrenheit), according to the Commodity Weather Group, potentially damaging for hard red winter wheat in the biggest-producing state.
The cold front has given impetus to a technical bounce this week when the most active CBOT contract hit its lowest since early February and spot prices touched the psychological $4 floor.
The chilly weather in the US Plains has added resonance to spring weather concerns in western Europe, where crops have faced frost in the past week on top of dry conditions, notably in France.
Farming agency FranceAgriMer on Friday reported a sharp decline in crop conditions for wheat, with the amount of soft wheat rated good/excellent falling to 78 percent from 85 percent in the week to April 24.
The most active CBOT corn contract was down 0.3 percent at $3.68-1/4 a bushel, but was still up 1.2 percent over the week. Soybeans dipped by half a cent to $9.57-3/4 a bushel, leaving them fractionally lower on the week.
Corn is under pressure from weather forecasts that scaled back rain expectations for early May, easing fears of planting delays.
Large supplies also continue to weigh on grain markets.
The International Grains Council, in a monthly report on Thursday, raised its forecast for the 2017/18 global grains crop by 4 million tonnes to 2.054 billion tonnes, down from 2.111 billion in 2016/17.
But a sharper projected fall in corn production compared with wheat could change the market balance next season, Commerzbank analysts said.