Using a 1-in. melon baller, scoop out 12 melon balls; chill airtight. Trim rind from remaining melon and chop the fruit to make 3 cups.
Distribute chopped melon among 3 standard-size ice cube trays. Drizzle with simple syrup and pour rosé on top. Freeze until melon is frozen (rosé will remain slightly slushy), at least 6 hours.
Spear melon balls on 4 to 6 short skewers. In a food processor, whirl half of rosé cubes at a time until smooth and slushy, scraping bowl and stirring as needed. Pour into glasses and set a skewer of melon balls across each.
MAKE AHEAD: The frosé cubes, up to 2 weeks, covered; for a completely smooth drink, partially blend them in the food processor, let stand a few minutes to soften, and blend again.
*To make simple syrup, heat 1/4 cup each sugar and water, stirring, until sugar dissolves; cool.